D2SA: Dual-Stage Distribution and Slice Adaptation for Efficient Test-Time Adaptation in MRI Reconstruction
Authors: Lipei Zhang
Rui Sun
Zhongying Deng
Yanqi Cheng
Carola-Bibiane Schönlieb
Angelica I Aviles-Rivero
Venue: NeurIPS 2025 poster ()
Keywords: Magnetic Resonance Imaging
Test-time Adaptation
Implicit Neural Representation
Self-supervised Learning
Primary area: machine_learning_for_sciences

Abstract: Variations in Magnetic resonance imaging (MRI) scanners and acquisition protocols cause distribution shifts that degrade reconstruction performance on unseen data.  Test-time adaptation (TTA) offers a promising solution to address this discrepancies. However, previous single-shot TTA approaches are inefficient due to repeated training and suboptimal distributional models. Self-supervised learning methods may risk over-smoothing in scarce data scenarios. To address these challenges, we propose a novel Dual-Stage Distribution and Slice Adaptation (D2SA) via MRI implicit neural representation (MR-INR) to improve MRI reconstruction performance and efficiency, which features two stages. In the first stage, an MR-INR branch performs patient-wise distribution adaptation by learning shared representations across slices and modelling patient-specific shifts with mean and variance adjustments. In the second stage, single-slice adaptation refines the output from frozen convolutional layers with a learnable anisotropic diffusion module, preventing over-smoothing and reducing computation. Experiments across five MRI distribution shifts demonstrate that our method can integrate well with various self-supervised learning (SSL) framework, improving performance and accelerating convergence under diverse conditions.

D2SA: Dual-Stage Distribution and Slice Adaptation for Efficient Test-Time Adaptation in MRI Reconstruction
Lipei Zhang"; Rui Sun Zhongying Deng', Yanqi Cheng', Carola-Bibiane Schönlieb', Angelica Aviles-Rivero
Department of Applied Mathematics and Theoretical Physics, University of Cambridge Shenzhen Future Network of Intelligence Institute
and Guangdong Provincial Key Laboratory of Future Networks of Intelligence, The Chinese University of Hong Kong (Shenzhen) 3 School of Science and Engineering, The Chinese University of Hong Kong (Shenzhen) Yau Mathematical Sciences Center, Tsinghua University
Abstract
Variations in Magnetic resonance imaging (MRI) scanners and acquisition protocols cause distribution shifts that degrade reconstruction performance on unseen data. Test-time adaptation (TTA) offers promising solution to address this discrepancies. However, previous single-shot TTA approaches are inefficient due repeated training and suboptimal distributional models. Self-supervised learning methods may risk over-smoothing in scarce data scenarios. To address these challenges, we propose a novel Dual-Stage Distribution and Slice Adaptation (D2SA) via MRI implicit neural representation (MR-INR) to improve MRI reconstruction performance and efficiency, which features two stages. In the first stage, an MR-INR branch performs patient-wise distribution adaptation by learning shared representations across slices and modelling patient-specife shifts with mean and variance adjustments. the second stage, single-slice adaptation refines the output from frozen convolutional layers with learnable anisotropic diffusion module, preventing over-smoothing and reducing computation. Experiments across five MRI distribution shifts demonstrate that our method can integrate well with various self-supervised learning (SSL) framework, improving performance and accelerating convergence under diverse conditions.
Introduction
Magnetic resonance imaging (MRT) captures detailed tissue structures using k-space sampling. In clinical practice, MRI is often under-sampled to accelerate sean time and reduce patient burden. However, under-sampling results in an ill-posed inverse problem, making accurate MRI reconstruction challenging [23]. Traditional compressed sensing techniques attempt to address this through iterative reconstruction algorithms [4, 5, 3, 28]. but these methods are computationally expensive and less accurate. Recent advances in deep learning have significantly improved both reconstruction speed and quality by learning direct mappings from raw data [18], such unrolled networks [27], plug -nd ald- frameworks [1]. and diffusion models [8].
Despite these advancements, deep learning models struggle with adapting to diverse clinical scenarios due to two primary challenges. Firstly, limited MRI data for model adaptation: MRI datasets are difficult to collect, making it challenging to generalise deep models without overfitting. Secondly,
'These authors contributed equally.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Target
Target
Target
Rapested taaiing
Ovanorouth
3. Singlessllee Approach
Seff-sperviised Approach with Few Data
6. 6.025A
Illustration of TTA strategies for MRI reconstruction under distribution shifts. (a) Single- slice methods require repeated training and are often unstable. Seff-supervised approaches with limited data may oversmooth or converge to incorrect mean/median of target domain. (c) D2SA first performs efficient, patient-level adaptation to unknown target distributions (blue path), followed by optional slice-level refinement guided by requirement from clinician (orange path and 8).
Figure I:
distribution shifts between training and test data: In weal-world deployment, MRI scans may be acquired under different conditions (e.g., scanner types, patient demographics), causing performance degradation due to mismatched data distributions between training and test sets [10, JJ. An ideal MRT reconstruction model should therefore balance three key goals for overcoming distribution shifts:
1) Strong adaptation to new distributions maintaining high performance despite distribution shifts. 2) Robustness to limited data preventing overfitting in data-scarce scenarios. 3) Fast convergence minimising adaptation time at test time.
Most existing methods focus primarily on distribution generalisation but fail optimise all three goals simultaneously. Test-time adaptation (TTA) techniques partially address this, i.e., they mitigate the distribution shift by updating models on the fly using only test data. Besides handling distribution shifts, batch-based TTA methods (e.g.. Noiser2noise [12], FINE [38], SSDU [36]) further enforce self-supervised learning across multiple slices to facilitate fast convergence. However, this batch- wise approach may overfit shared features across slices while ignoring slice-specific variations, leading to over-smoothed reconstructions. Conversely, single-slice-basee TTA methods [41, 34, 35] improve fine-gratd fine-graiedd adaptation but require repeated optimisation cycles, significantly increasing computational overhead. More recent liffusion-bascl models [2, 9] generate realistic slices for adaptation but are computationally expensive and prone to overfitting on smaller datasets.
To effectively balance all three goals, propose Dtal-Stage Distribution and Slice Adaptation (D2SA). D2SA leverages both patient-wise and slice-wise adaptation through a two-stage process. The first stage models single patient distribution using a small number of slices as prior knowledge. The second stage utilises this learned prior for fast adaptation to each slice, and further introduces an anisotropic diffusion (AD) module enhance denoising (21, 7] while preventing over-smoothing the structural details. It thus achieves fast adaptation with high reconstruction quality. Both stages treat each MRI slice as a continuous function rather than a static matrix, drawing inspiration from Functa [13] and implicit neural representations [25]) This function-based perspective allows us interpret distribution shifts as small function-level variations, e.g., functions with different mean/variance variables in the feature space. Owing to the adaptive mean/variance this function- centric approach can be efficiently adapted to new distributions without the need for extensive data for retraining. It also enables the plug-in in of networks at test time, thus highly flexible. Our novel approach ensures fast convergence, robustness to limited data, and strong generalisation to new distributions, addressing critical gap in MRT reconstruction research. Our contributions are:
Functional-Leve Patient Adaptation. We develop an INR-based strategy that learns patient's 's distribution from a small number of slices, with the INRs trained capture individualised mean and variance shifts for the second-stage fast adaptation.
Structural- Preserving Single-Slice Refinement. After modelling patient-level shifts, the pre-trained INR network rapidly refines each slice. We introduce a learnable Anisotropic Diffusion (AD) module maintain structural fidelity, reduce over-smoothing, and limit computation by freezing the main convolutional layers.
Seuutural-Preservinng
Extensive Validation. We evaluate D2SA on five distribution shift scenarios, using both UNet [26] and variational network [31]. Results demonstrate robust and efficient recon- struction across diverse clinical conditions.

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2 Related Work
Test-Time Adaptation (TTA) in Medical Imaging. TTA tackles distribution shifts by adapting pre-trained models using unlabelled test data [22]. A key challenge is constructing supervision signals without ground truth, typically addressed via consistency regularisation or self-supervised losses. Consistency-basel methods enforce stable predictions under perturbations. For instance, PINER [30] leverages implicit neural representations (INRs) to select resolution-consistent CT slices, while steerable diffusion models [2] ensure realistic reconstructions. Self self-suuerrised approaches define pretext tasks such as contrastive learning [19] or rotation prediction [17]. DIP-ITT [11] applies self-supervision for slice- wise reconstruction under shifts, and Meta-TTi [34] incorporates meta-learning to improve generalisation. In contrast to computationally expensive TTA methods, we propose dual-stage TTA framework that first performs patient-level adaptation to improve the
efficiency and robustness of per-slice refinement.
Implicit Neural Representations (INRs). INRs encode data as continuous functions, enabling compact and flexible learning. Functa [14] embeds entire datasets INRs for function-level learning, while DeepSDF [25] uses latent-conditioned autodecoders to model 3D shape fields. Biomedical INRs have been used represent detailed structures like airway trees [40], allowing for effective batch optimisation. Among various designs [15]. SIREN [29] remains strong choice for high-free fige-freueeccy data due its sine activation, and forms the basis of our patient- patient-wise adaptation module.
3 Problem Setup
First, MRI reconstruction is an inverse problem where the goal is to recover x" E C from under- sampled measurements y CM with M & N: y y Ax + e, where is the measurement operator, and represents noise. In multi-coil MRI, the acquired measurements for each coil follow:
y/ = M F S, x² + +,, i= 1=
(1)
where S, denotes the coil sensitivity map, F is the 2D Fourier transform. M is the undersampling mask which can be the ID cartesian mask, or others [37]. The individual coil images z, F F- are then combined via coot-sum-of-squall to reconstruct x.
Reconstruction is framed as optimisation problem:
1
f = arg min
2 | v13 + AR(z),
(2)
where R(x) encodes prior knowledge (c.g., wavelet é,, total variation, or CNN-based priors), and À controls the balance between data fidelity and regularisation. However, standard reconstruction models assume fixed distribution during testing. limiting their ability to generalise to new datasets or acquisition conditions.
Domain shifts from scanners, anatomy, acquisition protocols degrade performance. Existing TTA methods can address this but they rely on repeated single-slice training [11] or self-supervised learning on large datasets [12, 38, 36], lacking stability in data-scarce scenarios. To address this, we introduce a D2SA that first learns patient-wise distributions explicitly for better initialisation, enabling more stable and efficient refinement in the second stage.
4 Proposed Method
To address domain shifts efficiently, we propose D2SA, a dual-stage test-time adaptation (TTA) framework that avoids large datasets and slow repeated single-slice training. As illustrated in Figure D2SA consists of: (1) Patient-wise Distribution Adaptation, where MR-INR captures shared representations across slices and estimates variance (a) and mean (3) shifts; and (2) Single-Slice Refinement (SST), which refines each slice using a learnable anisotropic diffusion (AD) module with frozen convolutional layers. This design enables efficient adaptation with improved initialization.
4.1 Functional-Leve Patient Adaptation
In Figure 2, the MR-INR branch models the structure and distribution of patient- data. Inspired by Functa [13] and DeepSDF [25], which use INRs to encode data as continuous functions,
3

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Funetional-Level Patient Adaptation
b. Structural-Preserving Single-Slice Refinement
Latent code
7(0".5)
Random
Alvrotubee d
(02.0,) C.)
Pretreined Network
Affine
Affine
Layer
Layer
Figure 2: Overview of the proposed two-stage D2SA framework. (a) Functional-Level Patient Adaptation: An INR with Gaussia--inttalizzed latent code and random Fourier coordinates captures patient-level meenn/vrriace shifts. The & indicates trainable modules, including the "pretrained" network and the affine layer. (b) Structural-Presett
Single-Slice Refinement (SST): The main convolutional layers and learned latent code are frozen $ while a learnable Anisotropic Diffusion (AD) module and the INR refine individual slices, preserving structural details and finalising outputs via the affine layer.
Affine Layer (Transformation)
b. Anisotropic Diffusion (AD) Module
Difeencce ConN
GDC
ADC
Conv_layer
Jayur
VC
Fa
Comyral
VDC
HDC
Festure mane befone Inat lever
Figure 3: (a) Learnable affine transform scales feature maps by and / before the final layer. (b) Learnable AD module & refines images while preserving structures, with frozen convolution &
approach shifts from learning discrete datasets to learning in function spaces. This enables efficient adaptation to new unknown distributions, better handling of few-shot scenarios, and improved patient- wise learning capabilities.
In Figure 2.a, each slice in this patient set can we assume the prior distribution over ID latent code as zero-mean multivariate- maauisa with spherical covariance r²I. In this work, a is set to 0.01. The random Fourier coordinates will be calculated by geometric coordinates & of each slice. The input F for MR-INR is from concatenation of 2; and á.
(0, 24) [2t, cos Bo), sin Bo))]
(3)
where the transformation matrix B is sampled from Gaussian distribution N(O,w.)
the standard batch training protocol for all slices in each patient. In the After this step, corresponding latent code and Fourier coordinates are modulated and passed MR-INR branch, the
through SIREN [29] network fo architecture. The ability of SIREN and Fourier feature [32] to efficiently model target representation and stability has been shown in [15]. This MR-INR branch can be formed as:
[ a, fo(5((',)) W. (T n- o (o) x)) bn. ((+1) ()) = sin sinnW,h + b,).
(4)
Here, r; R.N, represents the 1th transformation layer. Each layer applies an affine transfor- mation with weight matrix W; E N.M; and bias b; E R followed by sine activation function. The final layer produces [ or, through three output heads. & with dimension (B, 2, H, W), rep- resents the predicted pixel intensity for MRI reconstruction. a variance shifts and 3 nonzero-mean shifts, with dimension (B, C, H, W), modulate feature maps before the final layer via an affine transformation, as shown in Figure 3.a, where C' is the number of feature channels. This formulation

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enables shared base network to model common structures while adapting to patient-specinn varia- tions, ensuring compact and efficient solution for TTA. Meanwhile, in the first stage, under-sampled MR images from the target domain are input into the network g8, initialised with source domain pre-trained weights, for TTA (gs - 9.+ Here, feature maps before last layer are extracted and adjusted via the affine transformation using or and 8, as illustrated in Figure 3.a.
The predicted MR image from this branch is used to compute the self-supervised loss Ceef such as Noiser2noise [12, 24], SSDU [36] and fidelity-based FINE [38]. The Leei combines with other two loss from MR-INR for joint optimisation. For MR-INR, we adopt a joint optimisation strategy similar to the auto-decodes framework [25], optimising both latent codes and network parameters. The optimisation for the first stage formulated as:
0, 2, Å arg min AINR 0,2,A
Σ
Li(Af(5(d)) :2),0),
(5)
+ Area
2
1212
+ Aself
Σ (x)))X
Larlo(ay 03, +2)).
Here, (Af(((( .2).0). ensures INR predictions aligning with MR signal consistency. The regularisation term - =1=111 constrains sparsity of the latent codes and prevents overfitting. The final
term updates weights 8 + A to adapt to patient-specific variations using self-supervised loss. Awtr.
Ainr and Areg used for balancing every loss contribution.
4.2 Structural-Preseriie Single-Slice Refinement Training
To refine MRI reconstruction at the slice level, we design a new SST strategy for fine-grained adjustments. Unlike patient-wise adaptation, which learns shared representations across slices, this stage optimises each slice independently to capture localised variations, as shown in Figure 2.b. The latent codes are frozen to preserve the leamed global prior information from patient-wise training. This prevents instability and avoids overfitting to slice-specific noise. Instead, the SIREN weights remain trainable, allowing the model to refine its implicit function for each slice. The affine modulation parameters a, B continue adjusting the final feature maps via scaling and shifting.
In the other branch, we adopt similar DIP-based TTT strategy [1 for SST. This approach leverages CNNs' strong image priors for structural preservation and optimises a self-supervised loss C on under-sampled test measurements. To improve efficiency, we freeze all convolutional layers except the final one and transpose convolutions, reducing unnecessary updates and accelerating optimisation.
A key challenge in batch training is its tendency to learn mean or median representations, leading to over-smoothing that can obscure fine textures and edges. This is critical in MRI. where structural details must be preserved. To address this, we introduce an Anisotropic Diffusion (AD) module, inspired by its preseriies properties in image denoising [7, 6]. As shown Figure 3.b, the AD module refines structural details while suppressing noise by integrating diffusion filtering into the adaptation process. Given an set of feature u, the AD equation is:
(uu)
= div Vu))
Vul) = 1+
(6)
0t
When the gradient magnitude is small ( (Vu) + 0), the diffusion coefficient g approaches 1, leading isotropic smoothing similar Gaussian filtering. Near object boundaries, where |uu] g approaches 0, preserving fine details. This allows AD to suppress noise effectively while keeping sharp edges, making it well-suited for edge-aware regularisation in reconstruction.
We enhance traditional convolutions by integrating difference- operators [7] that explicitly encode gradient information Vu. Five types of convolutions are introduced: Vanilla Convolution (VC), Central Difference Convolution (CDC), Angular Difference Convolution (ADC), Horizontal Difference Convolution (HDC), and Vertical Difference Convolution (VDC). These capture multiple directional gradients, incorporating concepts from Sobel, Prewitt, and Scharr filters directly into the convolution process [7]. The convolution operation is formulated as:
Vu Font = DConv((in) =
Σ
Pin K; = Fin Kests
(7)
5

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where Fin and Four represent input and output feature maps, respectively. Instead of separate convolu- tions, we merge all five kernels K; into a single equivalent kernel Kevi using re-parameterrsatioon technique. To improve efficiency, we reduce the number of output feature maps to 1/4 of the original channels, ensuring compact gradient extraction while minimising redundancy.
In calculation of AD equation (6), the computed Vu is used to determine the diffusion coefficient g. while the divergence div(-) is approximated via a 2D Laplacian kernel, which is more efficient to preserve spatial information than standard finite difference methods [39]. The output of the first equation in (6) is restored its original feature map dimensions using 1 convolution. Setting the diffusion step size At = 1 in (6), the updated feature maps are:
Uj+1 = 44 + At x1 (div (o((V,l)VV)))
(8)
In this stage, optimise the weights in MR-INR and the original network with AD module. The final loss function for the second step is:
X My Ag(A MilAyy,,o y. 6 + +AII
0, Å arg min
Σ (x
AINR Li (AS(F(0) 2),0), +
Σ (U))
0.A
MR-INR consistency loss
Self.sup loss
The first term is for measurement consistency, ensures that the MR-INR branch reconstructs MRI images accurately. The second term, Self-Suuervised loss, refines the prediction using measurement consistency. This formulation enables adaptive refinement while preserving prior knowledge learned from the first stage. Aselr and ÀINR are used for balancing every loss contribution.
4.3 Mathematical Analysis of Affine Adaptation
To motivate our use of affine transformations during test-time adaptation, we analyze a simplified setting under distribution shift. While our method uses nonlinear system, this linear case offers insights into how the leamed parameters a and B operate under such shift. Consider the test distribution:
(10) Here, U E Raxd is an orthonormal basis of the signal subspace, and Piq encodes the mean shift. Our goal is to estimate under this shift. The optimal TTA estimator and self-supervised loss are next: Proposition 1. An affine estimator of the form & aUUTy y minimizes the following self- supervised loss:
Q: - x= Uc uQ: c~N(00,1) z ~~,
Lss(a, B) = EQ [|x -uuu' +
- [I(a [L >1
2ad
(11)
Theorem 1. Minimizing Lss(ar 3) yields optimal parameters by solving the first-order conditions.
The gradients are:
ÖLss 2(3 pQ), da
0Lss = -2d(1 1 - a. + 2ads2
03
Solving these gives the optimal solutions a" Itsæ and B HQQ
These parameters decouple the effects of noise and mean shift: a" corrects variance, and 8 aligns the mean. They learned by minimizing the self-supervised loss under the test distribution. This analysis provides a clear intuition for our design: although the full model nonlinear, we apply the linear affine adaptation in feature space of MR-INR. More detailed proof and derivations in the Appendix. Next, our empirical results further confirm the robustness of this effective TTA approach.
Experimental Settings
5.1 Datasets and Experimental Settings
We evaluate on multi-coil MRI data from fastMRT [37] (knee, brain) and Stanford [16]. Each experiment defines source distribution S and target distribution T, measuring performance via

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SSIM, PSNR, and LPIPS. We consider two baselines: (1) U-Net [26]: 8 layers, 64 channels, trained with Adam [20] learning rate 10 10-8; (2) VarNet [31]: 12 cascades, 18 channels, trained with Adam at 10-1, All other training settings follow [11], using combination of supervised and self-supervised losses. We simulate 4x undersampling with ID random Cartesian masks and 8% auto-calibration lines, estimating sensitivity maps via ESPiRiT [33]. We examine five domain shifts: anatomy, dataset, modality, acceleration, and sampling, evaluating both out-of-distributtion (S + T) and in-distribution performance (see Appendix).
Anatomy Shift. Following in [11]. U-Net and VarNet are trained on fastMRI knee data as the source domain (S) and evaluated on fastMRI AXT2 brain data as the target domain (7). For TTA evaluation, we randomly select 10 subjects, resulting 110 AXT2 brain slices subsampled at 4x.
Dataset Shift. Following [11], we train both models on Stanford knee data (S) and evaluate on fastMRI knee data (T). We sample 20 patients from fastMRI, yielding 400 knee slices under the same 4x subsampling ratio for TTA evaluation.
Modality Shift. U-Net and VarNet are trained on fastMRI AXT2 brain slices (S) and tested on AXTIPRE slices (T), following the setup in [[]]. We randomly select 10 patients, yielding 110 AXTIPRE brain slices with 4x subsampling for TTA.
Acceleration Shift. Models are trained on fastMRI knee measurements acquired with 2 acceleration (S) and tested on the same set of knee slices with 4x acceleration (7), as in [1.]. We evaluate TTA on 400 slices sampled from 20 patients.
Sampling Shift. The uniform sampling presents more coherent artifacts that are more challenging to handle. We also train fastMRI AXT2 brain data subsampled using random ID Cartesian mask at 4 x acceleration (S) J. and evaluate on the same AXT2 slices sampled with a uniform 1D mask at the same acceleration rate (T). For TTA, we randomly select 10 patients, totaling 110 slices.
Additional details of stage-1 I and stage-2 training procedures are in the Appendix. Appendix is provided as separate file in supplementary materials.
5.2 Compared Methods
We compare D2SA with four representative test-time adaptation (TTA) baselines. DIP-TTT [1]] performs single-slice adaptation using Deep Image Prior (DIP). FINE [38] is batch-level TTA approach based on fidelity constraints. Noiser2noise (NR2N) [12, 24] and SSDU [36] are self- supervised methods that operate in patient-wise manner.
DIP-TTT follows its original setting, while FINE, NR2N, and SSDU are trained using the same configuration as the first stage of our method. To assess the benefit of MR-INR, we integrate it into FINE, NR2N, and SSDU for patient- wise adaptation. All resulting pretrained models- with and without MR-INR ARR-INR-are are then used in the second-stage single-slice refinement under the same setup as our stage 2. Models without MR-INR adopt only supervieed loss, similar to DIP-TTT.
We also include ZS-SSL [35], an augmentation-basee based self-supervised single-slice TTA method, Our preliminary results show that it is compatible only with unrolled networks such VarNet, and fails to generalise to end-to-end U-Net architectures. Detailed comparisons are provided in the Appendix. All experiments were run on a single NVIDIA RTX 3090 GPU. For timing, Stage inference time is measured as the total duration of 25 fixed training epochs. Stage 2 (SST) time is computed as the sum of per-slice training durations until early stopping, using the same validation-bar based strategy as in [11]. The final reported time combines both stages.
6 Results& & Discussion
Main results. Tables I and Figure 4 summarize the average SSIM, PSNR, LPIPS, and adaptation time for U-Net and VarNet under five domain shifts: Anatomy, Dataset, Modality, Acceleration, and Sampling. Across most settings in Table 1, +MR-INR+SST achieves consistent improvements over baselines. For example, in the acceleration shift, FINE+MR-INR (VarNet) improves SSIM from 0.696 to 0.791 and PSNR from 21.39 to 25.30. While MR-INR introduces modest runtime overhead. +MRI- PIRI-INR+SS +ST performances rival or exceed DIP-TTT in multiple cases (e.g., SSDU on anatomy shift, NR2N on dataset shift), while significantly reducing adaptation time (e.g. 17.1 vs. 52.5 mins/patient in anatomy shift). These results demonstrate the strong synergy between wate MR-INR adaptation and single-slice SST refinement.
7

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Method (VaSet)
Anatomy Shift Koce.
Dunaset Shift
Modality Shift
Accelenation Shift
Sumpling Shift
Stunford, foaMRR)
AXT2, AXTIPRE)
(S: 2x, 2:44k
Random, T: Uaifonu)
Zem-diling
0.77724 927-
0,747/34.850 353--
0.747/25 350-
0,754/3. 370 1964-
0.766/66 2801 13R-
Non: TTA
0,79223, 160,37
0,706/2.3500 365)
0,796/23 540.379/
0,761/23 04/0.32/
Q.11
DIP-TIT
0.878227 67A0, 312/52.5
7.70/2800000 293/41.8
867728 3997166
08815788
97.2
0 6500 254/38-9
BINE
870/24 01 543/9.9
0.780/76 7610
0821/76 180 1603.5
18066/1 5960 342/6 2
0.69221
365/1
TINE-MR
0.862/26.455 4510122841,7
0,795/26.444 4400,
0,80726.5000000
2.789/251000,22000
HINE
6.862/27.57A.
794/277777 721227772...00 294/20.3
0357225
0.823/28.
0,748/25. 276/488
FINEMM--NNKSSS
0.800/28.720022000
0167228
32/0337//21.8
0.829/28
0.82442H 4900 252222222222
0.822/23 9541.554444
0.798/26.59 2996.8
36824,
0.718/20 97A0,
0.60121
NRON-MR-INR
8.60626.00
20477
0833/3644400
4400 36944
0.806/25 42/0 201/7.6
0,78675 2400, 30644,5
NR2N-SST
0.83/22.720.301665
0. 0.798/27.784. 293/25.3
0.86228.1 17K0 1780.341/90.2
0.822/28.05000 291/64422
0.771/26,446 (6-122266666222222211 27667.1
NR2N-MR INR+SST
0.812/28. 76/0 281/2004
0.88928.300
36/03335/00.
0.826/28
89/02 272/43.1
0.822/28. 2412,241/25.2
SSDU
87730/20.7/0.33353
07727/2.434.54999
0,746/2. 2E8622.5900334144 341444
1.56/115.939044217777
0.483/17 91356....3
SSDUHMMRIIN
1.821/2.2501.. 35085.
7.764211 66700 33077.5
0.79622 39004 8
0.772/11 57.1 358/7.9 9
0.554/18 S8a 40935,
SSDU+SST
0,879/27.6540 65-0. 1/066.33
0. 1.789/26. 75/0. 295/24.9
0,857/28 0770 200.343//9.4 4
O. 0.800/28. 06600 290/134.3
0.736/24.54 5400 263/50.5
SSDU+MR-
D. 0,806/28, (6/0) 24
0.86228.090 09K0 09K0.44/29. 3
0,826/28 22.2226222222644655 25644.2
0.80028.21100 254.2225
Table 1: Performance comparison of VarNet methods under different domain shifts. Each cell
presents (SSIM t PSNR + LPIPS / Time (mins/patient) )). The family of proposed methods
incorporates a self-supervised learning framework, combining MR-INR-base R-baedd patient-wise adaptation with single-slice refinement using pre-trained patient-wise models.
Ulit:: PSNA cain Adding MS. INi Module Across Stratagies and Domain Shifts Stage
SS FIVE Farilty Stape 1
SSIN: HRIN Familyy Stage
SCIN: SCOU Family:: Stage
3.49
3,00
6-41
6:00
6:20
Analoryy
Salanol
Peaulity Ascoisation Sampdrg
Uldt: Intercees Time LMPS
FIEE Fumily: Stage 1.
SSIM: NR2N Puriity: Stuge
SSIP: SEDU Family; Stage
Stage
Figure 4: Perforrance Analysis of U-Net under Different Domain Shifts. Top-left: PSNR gain from adding MR-INR across FINE, NR2N, and SSDU in stage 1, with the largest gain in modality shift in most strategies. Bottom-left: LPIPS vs. inference time trade-off showing that +MR-INR+SS achieves higher quality with reduced time comsumption compared to DIP-TTT and normal +SST. Right: SSIM across five domain shifts for each SSL family, visualized patient-level (Stage 1) and after slice refinement (Stage 1 Stage 2). MR-INR consistently improves performance across domains, and combining it with SST further enhances SSIM.
Figure further illustrates the effectiveness of MR-INR. The top-left plot shows PSNR consistently increases across most TTA families, with the largest gain in the sampling shift. The bottom-left trade-off curve shows MR-INRSSST achieves lower LPIPS with lower cost than DIP- Radar plots confirm SSIM gains from Stage (MR-INR) and further improvements when combined with Stage (SST). Quantitative results of U-Net results and performance analysis of VarNet are also provided in the Appendix 8.
Additional findings on experiments show increased undersampling or new anatomies, modalities and datasets show that non-TTA often outperforms zero-filling, especially for U-Net. However, under large mask shifts, unrolled models like VarNet suffer more severe degradation without adaptation, underscoring the necessity of TTA in such cases.
Qualitative Results. Figure 5 present visual comparisons of reconstructed images for the FINE- based UNet methods in the anatomy shift. More results of other distribution shifts and VamnNet are provided in the Appendix. sulf-suup methods without MR-INR (e.g., FINE [38]) may risk over- smoothing when confronted with limited data, as highlighted in the error maps. While FINE+SST improves over FINE by incorporating single-slice adaptation, lacks the AD module, leading to over-smoothing and loss of structural details. Our proposed approach, which integrates MR-INR with SST and AD, effectively balances adaptation and detail preservation, reducing hallucinations and enhancing reconstruction quality.
8

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Ground Truth
Zoro
Non
DIP-TTA
FINE
FINE+MRINR
FINE-9TT
Figure 5: Comparison of different frameworks in UNet under anatomy shift (Knee to Brain) using the FINE method. The first row shows reconstructed MRI images, while the second row presents residual maps between reconstructions and full-sampled MRI. The proposed method (far right) achieves the lowest residuals, indicating improved reconstruction accuracy.
Ablation Study. We conduct a comprehensive ablation to disentangle the contributions of MR- INR, SST, and AD to adaptation performance under anatomy shift (Table 2 and Table 3). For both U-Net and VarNet backbones, introducing MR-INR on top of FINE yields clear PSNR improve- ments (e.g., +0.5 dB on U-Net), demonstrating that the lightweight latent code provides effective patient-specific adaptation with negligible parameter increase. Further integrating SST significantly boosts performance but comes with increased inference time, highlighting its complementary role in capturing slice-level variations. Importantly, incorporating AD alongside frozen CNN achieves the best trade-off between performance and efficiency (27.71 dB / 12.1 min on U-Net; 27.6 27.68 dB / 17.1 min on VarNet), outperforming both purely patient-wise or slice-wise training. This suggests that AD effectively compensates for the lack of full fine-tuning, particularly in constrained adaptation settings, and enhances the robustness of MR-INR+SST pipelines. Interestingly, while AD brings limited improvement when used with fully trainable CNN, it yields notable gains when the CNN are frozen. This highlights AD's effectiveness in constrained settings, where its adaptive capacity compensates for the lack of end-to-end fine-tuning. This effect is further supported by the results in the last two rows of the table.
We conduct sensitivity analysis on the AD step size (Table 4). We observe that reconstruction quality stable across a wide range of step sizes, with the best PSNR/SSIM obtained at 1.0 and only marginal degradation at smaller values. Mcanwhile, LPIPS improves slightly the step size decreases, indicating a tunable trade-off between fidelity and perceptual similarity. This robustness suggests that AD is insensitive to moderate hyperparameter variations, which is desirable for test-time deployment. Similarly, Figure shows that adding directional and adaptive priors steadily improves PSNR and SSIM, further validating the effectiveness of the adaptive components.
Additional results on in-domain adaptation, statistical analysis, sensitivity analysis, and more visual- izations are provided in Appendix 8.
7 Conclusion and Limitation
We presented D2SA framework, a test-time adaptation framework that improves MRI reconstruction under distribution shifts. D2SA combines patient-wise MR-INR for modeling mean/variance shifts and single-slice refinement via learnable AD module. This dual-stage design enhances general- isation, preserves structural fidelity, and accelerates convergence. Extensive experiments across five domain shifts demonstrate that D2SA consistently outperforms prior TTA approaches in both quality and efficiency. Ablation studies further validate the contributions of MR-INR, AD, and frozen layers in balancing performance and runtime. While D2SA reduces adaptation time and improves generalisation, several limitations remain. First, current evaluations are limited publicly available datasets; further validation on real-world clinical undersampled MRI is necessary. Second, the framework operates on 2D slices eereennddnnyy-eeendninii
exploit full 3D spatial correlations a natural next step. Finally, integrating stronger priors (e.g., diffusion models) and developing online or incremental learning strategies could further enhance adaptability and prevent forgetting when adapting to continuous patient streams.

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Ablation (UNet)
PSNR
Params Time J
Ablation (VarNet)
PSNR 1 Params / Time
Patient-wize training
Patien-wiis inaiiiing
FINE
25.98/ 31.02
FINE
24.01 11.01/299455 29:4//995/33
+MR-INR (# istent code)
26.37 31.29 5.3
+MR-INR ( latent code)
26.37/ 13.3
+MR-INR ( latent code)
26.48 /31.9 /.5
+MR- ( latent code)
26.45 29.69 147
Single-slice training without stage I +SST &6
Single-siiee training without stage I
(A)
27.31 / 17.62 18.7
+SST ( cnn & AD)
27.50/ / 16.74 56.8
Single-slice training with stage
Single-sliee training stage
+SST ( cun)
27.22/ 31,02 11722
+SST cnn)
27.57 / /9:45 53.6
+SST & can AD)
27.37 / 17.62 /22.6
+SST @ cnn AD)
27.58 / 16.74/ 53.3
+MR INR-SST (4 cnn)
27.65 31.29 23.65
+MR INR+SST (4 cnn)
27.68 / /29.99 /2.9
+MR-INR-SST con- AD)
27.54 27,54/446.13 15777
+MR-INR+SST (4 cno+ AD)
27.61 / /43.79 34.0
+MR-IN&&- (
27.41/ / 17.62 14.5
27.63 16.74 27.8
+MR-INR-SSIIC + can)
27.38 3.05 17.5
+MR-INR+SSTI cmn)
27.45 2.88 21.6
+MR-INR-SSTI B
27.71/ / 17.89 12.1
-MR-INR+SST 4M
27.68 / 16.98 17.1
Table 2: Ablation study on MR-INR and AD under anatomy shift (U-Net). Each row reports PSNR 1, parameter count (Millions) 4. and in- ference time (min/patient) 4. The latent codes only have 1408 parameters in this shift. Stage 1 compares MR-INR variants; Stage 2 evaluates SST with and without frozen MR-INR and AD.
Table 3: Ablation study on MR-INR and AD un- der anatomy shift (VarNet). Each row reports PSNR t. parameter count (Millions) 4, and in- ference time (min/patientt) L. The latent codes only have 1408 parameters in this shift. Stage compares MR-INR variants; Stage 2 evaluates SST with and without frozen MR-INR and AD.
AD Step Size
PSNR t
SSIM f
LPIPS
Diff Conv Comparison (SSIM PSNR)
1.0
27.71
0.876
0.320
0.876
27.55
0.1
27.38
0.874
0.322
0.874
27.50
0.01
27.36
0.874
0.323
SSIM
SSNR
0.872
27.45
Table 4: Sensitivity analysis of AD step size. Re- construction quality remains stable across step sizes, with the best PSNR/SSIM at 1.0 and slightly improved LPIPS for smaller values, indicating a tunable fidelity-perceptioo trade-off and robust- ness to hyperparameter variations.
0.870
27.40
HDC+VDC
COC+ADC
Kernel Type
Figure 6: Ablation study on different kernel designs difference convolution in terms of SSIM 1 and PSNR t. Progressive improve- ments are observed from Vanilla to HD+VD, CD+AD, and ours, demonstrating the effective- ness of direction-awan and adaptive designs.
Acknowledgement
LZ gratefully acknowledges the financial aid award from NeurlPS and the travel support from DAMTP and Queens' College. RS acknowledges the support from Future Network of Intelligence Institute, The Chinese University of Hong Kong (Shenzhen). 7DD acknowledges the support from Wellcome Trust 221633/7/20/Z and the funding from the Cambridge Centre for Driv-Driven Discovery and Accelerate Program for Scientific Discovery, made possible by a donation from Schmidt Sciences. YC funded by an AstraZeneca studentship and a Google studentship. CBS acknowledges support from the Philip Leverhulme Prize, the Royal Society Wolfson Fellowship. the EPSRC advanced career fellowship EP/VO29428/1, EPSRC grants EP/S026045/1 and EP/TO03553/1, EP/NO14588/1, EP/T011961/1, the Wellcome Innovator Awards 215733/2/19/Z and 221633/2/20/2/ the European Union Horizon 2020 research and innovation programme under the Marie Skodowska-Ci -urie grant agreement No.777826 NoMADS, the Cantab Capital Institute for the Mathematics of Information and the Alan Turing Institute. AIAR gratefully acknowledges the support from Yau Mathematical Sciences Center, Tsinghua University.
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D2SA: Dual-Stage Distribution and Slice Adaptation for Efficient Test-Time Adaptation in MRI Reconstruction- Appendix
Contents
Training Details
22
Supplementary Quantitative Results in OOD Shift
22
Comparison ZS-SSL
24
D Other Ablation Studies and Sensitivity Analysis
25
Quantitative Results in Same Domain Shift
26
F Mathematical Analysis for Proposed Method
27
FI Test Distribution and Problem Formulation...
27
F.2 Self-Supervised Adaptation by Affine Transformation
27
G Supplementary Visualisations
30
G.I UNet
30
G.2 VarNet
32
21

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A Training Details
This section outlines the key configurations, optimisation strategies, and architectural choices em- ployed during training.
Patient Adaptation. We train the MR-INR-based model using a batch size of 2. Two Adam optimizers are used: one with learning rate of 10 for the MR-INR weights and the base network, and the other with a learning rate of 10-3 for the learnable latent code. The training runs for 25 epochs, with convergence typically observed after 20 epochs. The ID latent code (size 1 128) is initialized using zero-mean multivariate Gaussian distribution with standard deviation σ = 0.01.
Stage 1: Functional-
For the SIREN architecture [29], we use 4-layer MLP with 256 hidden units per layer and follow the weight initialization method from the original paper. In U-Net, the loss coefficients in this stage are set to: Aseff = 1, AIRR = 1, and Areg le For VarNet, we use Aself 1, ANR = 1e- and
Areg = 1
Stage 2: Single-Slice Refinement. In this stage, we refine each slice using a learnable Anisotropic Diffusion (AD) module while keeping the original convolutional layers frozen. We use the Adam optimizer with a learning rate of 10 and train for up to 1000 steps.
Following the self-validation strategy in [II]. we reserve 5% of the k-space signals for validation. If the validation error does not decrease in fixed iterations, the refinement process is terminated early. For early stopping, we apply a sliding window of size 30 to monitor the moving average of the validation error for methods including FINE, NR2N, and SSDU (with and without MR-INR).
DIP-TTT uses a sliding window size of 100, as defined in the original repository [1]]. The loss
coefficients for U-Net are Aselr 1, AIRR and for VarNet, they are A 1, AINR le-3
Mask Setup. First, general under-sampling mask set by using 1D Cartesian masks with an acceleration rate of x4 and 8% auto-calibrating lines.
For Anatomy, Dataset, and Modality shifts, the same x4 random ID Cartesian mask applied to both source and target domains. For the Acceleration shift, the source model is trained on MR signals under-sampil sampled at x2 using the same 8% calibratiirttionn strategy, while the target domain uses x4 mask with the same random seed to simulate the shift. - For the Sampling shift, the source domain uses a random x4 mask, and the target domain uses a uniform x4 mask, both with 8% calibration lines. Specifically, for in-distribution testing under sampling shift, we apply different random seeds to generate the masks while keeping the sampling strategy (x4, random) unchanged.
All mask generation and TTA implementation are provided in the demo script.
B Supplementary Quantitative Results in OOD Shift
Performance comparison of UNet methods under different domain shifts. Table 5 reports comprehensive and direct quantitative comparisons of UNet-based reconstruction methods under five distinct types of domain shift: anatomy, dataset, modality, acceleration, and sampling. Our proposed two-stage strategy combines patient-level adaptation (MR-INR) and slice-level refinement (SST with AD module). It consistently achieves top or near-top results across SSIM, PSNR, and LPIPS. Meanwhile, the inference time remains practical and competitive. Notably, the two-stage models yield especially strong improvements under more challenging shifts such as dataset and modality, where domain discrepancies are typically larger. These gains demonstrate the benefit of globally shared representations learned during patient-level adaptation, which are then effectively refined with localized slice-level refinemennt training. Furthermore, compared to strong baselines like DIP-ITT and one-stage TTA methods (e.g., +SST), our models exhibit improved stability (lower I.PISS and higher sample-level fidelity (SSIM/PSNR), highlighting the robustness and generalization capacity of our hierarchical test-time learning approach under OOD scenarios.
Visual Analysis of VarNet Performance Across Domain Shifts. Figure 7 provides a detailed visualization of VarNet's performance under various domain shifts based on the Table of VarNet in main paper. The bar chart (top-left) highlights PSNR gains achieved by incorporating MR-INR in Stage across FINE, NR2N, and SSDU training strategies. Acceleration and sampling shifts benefit the most, reflecting MR-INR's ability to capture cross-slice anatomical consistency in challenging
22

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Method (UNet)
Anatomy Shift Koce.
Dunaset Shift
Modality Shift
Accelenation Shift
Sumpling Shift
Stunford, foaM
AXT2,
AXTIPRE)
(S: 2x,
Randomm T: Uaifonu)
Zem-diling
0.737/24 327,-
0,754/2.3300
0.747/2 74, 3505
371/0 1964-
0.765/26 2801 338-
Non: TTA
062521.770..0 7700-85/
0,55921
0,794/27 2012-11-
0,72623,3700 296
0.25526. 978
DIP-TIT
0.89927 (500, 922/42.1
88107880060 25644088
084627.666 610 361/315
0.8152279330 29005,
9600 314/37,1
BINE
8.84//5 98/0, 35
7066676 5410 31065
0,25/26, 710 977/5
0,783/25
75/0, 1.6
0.872/27
314/5,
TINE-MR
0.845/26 576055665,5
0835/26.5110.77226
0.793/26 254072267.0 7,0
0.876/238 2441622322443333/33.
HINE
0.8K8227
327/1 7-2
8287728
283/21
0 720 293/21-9
0.823728
0,891/29 (1200 514/18,4
FINEMMK-INKSSST
0.876222.7100
0.829928.344
1861/27.9300222
0.825/28
0.895729,0500
0.836/25
0.796/26.114
516669
0 38366
0.781/26 2000,
6.859/26 911.
NRON-MR-INR
8.849/26 11/0. 346/5.7
0,708/26 42/0. 317/7,
0.829/66 640 381V7.3
0,791/26 37/0, 301/7.5
0.867/27.33M,
343/5,7
NR2N-SST
0.808/27 3541332//11.
0.825/28. 23/0 254/22.5
0.84427.6698
001-227.900.28//221 284/22.6 6
0.822/28.00A. 2911/277
0,892729,05 00....5550.
NR2N-MR INR+SST
1.S70/2733/000222
0.800/88.300
279//66
0.8622279989 98/02/9/9922111
0.825/28.50
2010228800002277233000 287/31.7
0.895/29.12 1200,313/122
SSDU
0.811/24.220.35330
1778/22.2770.54447
0.819/4,2700.380 33971
0.789/2503-0034400
0.856/24.550 249.544999.
SSDUHMMRIIN
0,861255 1840. 348/5.6
0.789/22.445 4500 3308.0
0.88224.99700 385/7.4
7979222 7841 344/7.7
0.873/266 1.0 84776.6
SSDU+SST
0,871/25.122 1700. 349/255
0. 6257288. 35,0, 284/206
0854227.11.32277777
7
0. 6232228 (77A0 290/1 39.8
0,893/29 (2200 315/28.1
SSDU+MR-INR INR+SST
2597/27.4400,222111
D. 828228. 2677188718.9
ORRIV28.040..00 287/174
0,826/28 (2302266220222666 286/2622
0,897729 3400,310V144
Table 5: Performance comparison of UNet methods under different domain shifts, Each cell presents
(SSIM f / PSNR t LPIPS / Time (mins/patient) 4). The proposed methods combine MR-INR-
based patient-wise adaptation and single-slice refinement.
Varllet: PSUR Gain by Adding MR-IKR Madule
SHIM: FINE Familyy;
SEIE: NRON Family: Stage
SGIM: SEDU Familyy Stage
Across Strategies Domain
100J
jubbi
1.c0
0.00
Sampling
(MA22 family acreas Donann Shitko
interence
SSIV: TIME Farily: Stape
SSIM: HA2N family: Stape 1 Stage
SGIN: SCDU familyy Stage
intespatire)
Figure 7: Perforrancee Analysis of VarNet under Different Domain Shifts. Top-left: PSNR gain from adding MR-INR across FINE, NR2N, and SSDU in stage 1, with the largest gain in modality shift in most strategies. Bottom-left: LPIPS vs. inference time trade-off showing that +MR-INR+SST achieves higher quality with reduced time comsumption compared to DIP-TTT and normal +SST. Right: SSIM across five domain shifts for each SSL family, visualized patient-level (Stage 1) and after slice refinement (Stage 1 + Stage 2). MR-INR consistently improves performance across domains, and combining with SST further enhances SSIM.
contexts. The LPIPS vs. inference time plot (bottom-left) illustrates that MR-INR+SST strikes a favorable balance between reconstruction quality and computational efficiency, outperforming DIP-ITT and conventional SST in both metrics. Radar plots (right) further validate hicrarchical design: Stage improves SSIM through patient-level adaptation, while Stage 2 refinement with SST delivers additional performance boosts. These results reflect trends observed in Figure of performance analysis on UNet and confirm that our framework generalizes effectively to VarNet, enhancing robustness and generalization under all OOD shifts.
Distributional Analysis. To further assess the robustness of our method, Figure 8 presents violin plots of adjusted SSIM, PSNR, and LPIPS metries under two representative domain shifts: accel- eration (top row, Knee dataset with UNet) and sampling (bottom row, Brain dataset with VarNet). I and a denote the mean and standard deviation of each metric across slices per subject. Adjusted values are computed as μ - 0.5g per subject, considering both and emphasizing performance stability across slices per patient. Notably, SSDU+MM-INR-SST consistently outperforms both DIP- and SSDU+SST across all metrics. Improvements are statistically significant in most cases, particularly for PSNR and LPIPS (p < 0.01, Wilcoxon signed-rank test), highlighting our framework's ability to deliver high-fidelity and stable reconstructions, These results reaffirm that the two-stage strategy
23

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(ji under Accelleation Shift (Stage 1+22)
Adjusted (U)
0.5e)
under Accoleration Shift (Stage 1+2)
under Acceleration Shift (Stage 1-2)
32.3
Adjurtee 550M
adjueted B5MM
0.55
Adjueted
0:30
0.75
6:20
0.20
DFP-77
555U
5500 55T
DFF-77
5500
550 551
VarNet:: Adjusted SSIM 0.5o)
VarNet: Adjusted PSNR 0.5e)
VarWet: Adjusted LPIPS -0.5g
Sampling Shift
Sampling Shift
Shift
0.223
Adjusted SSIM
0.
adjucted POWK
Adjusted Lpips
0,997
6,279
6,20
0.22
6.200
DENTTT
S62U-66T
Figure 8: Comparison of model performance under domain shifts in acceleration (top) and sampling (bottom). Violin plots show the per-subject distributions of adjusted SSIM (1), adjusted PSNR (1), and adjusted LPIPS (L), where each adjusted metric is computed as 0.5g, with and denoting the mean and standard deviation of each metric across slices per subject. Three test-time strategies are evaluated: DIP-TTT, SSDU+SST, and SSDU+MR-INR+STE acceleration shift on the Knee dataset using UNet, while the bottom row corresponds sampling shift on the Brain dataset using VarNet. Mean values are marked within each violin. Statistical significance of SSDU+MR-INR-SST compared baseline methods (DIP-ITT and SSDU+SST) is indicated by (p < 0.05) or (p < 0.01), based on Wilcoxon signed-rank tests.
The top row presents results under
(+MR-INR+SST with AD module) offers superior stability under diverse and challenging OOD shifts.
C
Comparison to ZS-SSL
Recent progress in TTA MRI reconstruction has introduced zero-shot paradigms such as ZS-SSL [35], which train directly on undersampled measurements from a single subject. While effective in few data cases, ZS-SSL reconstructs each slice independently, partitioning and augmenting available k-space into training, loss, and validation sets. This design can limit the model's s ability to capture shared anatomical representation.
Another representative method, DIP-TTT [11], improves upon the original Deep Image Prior by incorporating early stopping to stabilize optimization during test-time training. However, similar ZS-SSL, it operates slice-by-slice and lacks modeling of inter-slice spatial dependencies. While DIP-ITT has been shown to outperform ZS-SSL under anatomy shifts, broader comparisons across other domain shifts are missing.
In contrast, our proposed approach adopts a two-stage test-time adaptation strategy: (1) MR-INR performs subject-level adaptation by leveraging all patient scans to capture shared anatomical structure and slice-wise relationships, and (2) SST refines each slice independently via AD module. This hierarchical modeling allows us exploit both global context and local detail refinement during inference.
Table 6 presents quantitative results under five domain shifts: anatomy, dataset, modality, acceleration, and sampling. ZS-SSL shows competitive performance under anatomy and modality shifts, but does not achieve surpassing on all metrics and spends more time to converge. It lags behind our methods in all other settings. Our MR-INR+SST framework consistently achieves ofate-of-thh-an results across metrics and shifts. Furthermore, it significantly reduces inference time (e.g., 17-25 min vs. 100+ min for ZS-SSL), highlighting its practical applicability. More details about the the comparison on visualisation in the last aection-Supplementan Visualisations.
These findings suggest that the hierarchical design of our two-stage adaptation better suited to handling diverse and challenging distribution shifts than methods relying solely single-slice
24

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reconstruction. By explicitly modeling cross-slice dependencies in Stage I and adapting locally in Stage 2, our method achieves strong generalization and efficiency in real-world deployment scenarios.
Method
Amatomy
Dutaset
Modullity
Accelcration
Sampling
(8) Knoc, T: Bosin)
(8) Stanford, (axMMRT)
(8) AXT2, T: AXTIPRE)
(8) 2x, T: 4x)
Rundom, T: Uniform)
Zero dilling
0.257/24.000.222
0.747/25.7100.8000 2100.300-
0.754/2-7701.990
0,70622.2500 2000000250.333
Non TTT
0,799233, 170
2.706/2.35/0..665
0.796/23 500.379/
0.761/23 0001/3300/0.37//
0.111/10.0000560
DIP
0.878/27.674 372.222
0.298/28.12/029929 292/61
0.867/28.3300 330.377/166
0.15/28.255 2015528.2550.. 285/1 59.2
0.77 65/0, 254/38.9
75-SSL
8,84422 0770 31499.5
0745/21.9330 365/1
0.86825 338/102
0,251/11 381/167.4
0.734/24 3000 306/52.2
FINE-SST
0.8 88222 5760, 1/55.
0,794/27.723 7200 294/2011
0.857788 08/0 345/70
0,82378 1700 788261.8
0.748/25 1&0 276448..
NR2N-SST
0.833/27.7200. 720.332666033 9
0.798/27.788 211.77880222222
0.86928. 17/0.241/80.
0,822288 (0000000000000 1900,291199,
0.771//26466
(6/6/776/57.1
SSDUASST
0885728.1770044488
(4700333335.. A43933.4
0308/28.0680222 293/1 54,2
0.736/24
24122448440-0 256/5055
RINE-MRINR-STT
8.833/7.6600 9197777777777.
08088/5 728772200000 226/188
0.8677X 520. 3877218
0.22 640.476444.5
0.824/28.88 232322222 232/22.1
MRON-MRINR-SST
6.54/2..81 30.33/118
0.812/28 26/0221//0044
0. 2.868788 35/ 336/20.3
0.8 0,82628 620 2
0,802/28 4010 241/2.2
SSDU-MRINR-SST
0. 850/27 367.3
0.808/8. 16/0 290/214
0,863778 0.86177.09003440 094.334/29999
0 0.826786220.6855 7867665555
0.300/28.1//..222 254422551
Table 6: Cross-domain evaluation under five domain shifts: anatomy, dataset, modality, acceleration, and sampling. Each cell shows the model performance in format SSIM (t) PSNR (f) / LPIPS (L)
Time (mins/patientt (4). Rows shaded in light red highlight our proposed MR-INRRSST methods, which achieve consistent improvements across shifts with notably reduced inference time.
D Other Ablation Studies and Sensitivity Analysis
Choice of INRs To clarify our choice of SIREN as the INR backbone in MR-INR, we conducted an additional ablation comparing different INR backbones under both patient-wise (FINE+MMR-NNR and single-slice (aaill--siceFFINBBAA (FINE-MR-INR+SS) training. Results are summarized below:
Backbone (Stage 1)
/SIM//PSNRY LPIPS.
Backbone (Stage l+2)
SSIM / /PSNR1 1 /LPIPS)
WIRB
0.839 / 25.78 0.355
Finer WIRE
0,873 22 0.323
Fincr
0.845/ 26.05 / 0,350
0.872 27:44 0.321
RPE + MLP
0.845 25.76 0.349
RPE + MLP
0,864/ / 27.22 0.326
SIREN only
0.845 26 16/ 0,344
SIREN only
0.874 / 0.322
Ours (PE+SIREN)
0.845 / 26.37 / 0.346
Ours (PEASIREN)
27.71/ 0.320
Table 7: Sensitivity of INR backhone choice under patient-wise (Stage 1) and single-slice (Stage 1+2) Refinement.
Our design combining random Fourier positional encoding with SIREN consistently yields the best or near-best performance, especially in perceptual quality (LPIPS). While Finer offers frequency adaptability, its more complex architecture increases overhead without clear performance gains; WIRE, though efficient, suffers from unstable convergence and limited representation in medical shift settings. Compared to INCODE, our SIREN-based MR-INR avoids the need for pretraining, supporting our lightweight, plug-and-play adaptation objective.
Loss Weight Ablation We further evaluate the sensitivity of the framework to different loss weight configurations for Stage (Asetr, AINR. AReg) and Stage 2 (Asetr, AIRR) (Table 8). Overall performance remains stable across wide range of À values, demonstrating the robustness of the training objectives. However, setting AINR too low (e.g.. 0.1) leads to notable degradation, especially in Stage and LPIPS in Stage This aligns with the key role of MR-INR in capturing patient-level distribution shifts, where sufficient INR loss weight is critical for effective adaptation.
Stage
A Settings
PSNR 1
SSIM 1
LPIPS
1/1/le/
0.832
Stage
//0.1/le
23,85
0.823
0.386
1/1/0.1
24.00
0.822
0.388
1/1
0.860
Stago
1/0.1
28.00
0.861
0.356
1/0.01
27.99
0.861
0.350
Table 8: Ablation of loss weight combinations, Performance stable across a wide range of values, but mild degradation when ÅINR is too small.
25

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Hyper-parameter Sensitivity. We evaluate the sensitivity of MR-INR (Stage 1) and SST+AD (Stage 2) to key hyperparameters, including latent code size, INR depth, and initialization scale (Table 9). The performance across PSNR, SSIM, and LPIPS remains remarkably stable, with less than 0.15 dB variation in PSNR and negligible LPIPS differences. This robustness indicates that the method is largely insensitive to moderate hyperparameter changes, making it well suited for deployment without extensive tuning.
TTA Stage
Hyperparameter
SSIM 1
PSNR
LPIPS 4
Latent Code Size (64/ 128/////222 (56)
0.849 0.849/ /0,850
26.37 26.47
0.345/0.34/ 00333
Stage
INR Depth (3 ()
0.842/08455/ /0,848
26.34 26.37 26.44
2.34500.36- / 00334
Init Sid (0.1 0000 / 0.001)
0.845 / 0,845 /08847
26.50/ 26.50/26.37/ 22.37
0.346/ / 00.345
Latent Code Size (64/ 128/ 256)
0.876 / 0.876 / 00877
27.53/27.71 27.53
0.323 0.320 / 0.320
Stuge
Depth (3 /4455) 5)
0.874/0. /.876/ /0.877
27.54 27.56
0.321 0.320 103319
Init Std (0.1 0.01 / 00001)
0.876 0.876/ / /0.815
27:53127.771 27.52
0.321 0.3200 / /0.322
Table 9: Hyperparameter sensitivity of MR-INR (Stage 1) and SST+AD (Stage 2). The method remains stable under variations in latent code size, network depth, and initialization, with PSNR fluctuations < 0.15 dB and negligible LPIPS differences.
E Quantitative Results in Same Domain Shift
In-domain Generalization Analysis. Table 10 reports the performance of UNet-based reconstruc- tion methods evaluated under same-domain (in-domain) settings across five shifts: Brain, fastMRI, AXTIPRE, 2x, and Random. As expected, most methods perform better under in in-domain testing compared to distriititiiittinnnn (OOD) settings, with consistently higher SSIM and PSNR and lower LPIPS scores. Among the baselines, DIP-TTT demonstrates strong performance, especially in settings like Brain and AXTIPRE. However, it comes at a significantly higher inference cost, as reflected in its per-patient runtime.
Notably, our proposed two-stage pipeline (MR-INR+SST) achieves the best or second-best scores across almost all shifts, outperforming both FINE+SST and DIP-TTT in both fidelity and efficiency. For instance, in the sampling in same domain shift, SSDU+MR-INR while maintaining reduced LPIPS and halving the inference time compared to DIP-TTT. Furthermore, combining patient-level modeling (MR-INR) with slice-level SST refinement results in consistent performance gains over single-stage variants, demonstrating the benefit of hicrarchical adaptation even in-domain.
improves SSIM and PSNR
This table highlights the robustness and generality of our framework: even when domain shifts are minimal in some cases, dual-stage adaptation continues to yield meaningful improvements in both reconstruction quality and computational efficiency.
Method (UNee)
Brain Brain
faiMMI fasMMRI
ANTIPRE AXTIPRE
2x
Random Randon
Zero- filling
0.737/24 500.385.
7747725.7000.28 3501.
01466266520022222 226/
0.811/26.320.33
Non-TT
0.822/26. 33322/665000.560 500.358/
0.559/2L88/04500
0,799/26.08/..990
0.149/15.74005500
0.76425.8700311
DIP-TTT
0.876/7.4510 323/46,1
0.808288 281/62.9
0.85827 3780335/15.11
0.834/28.634 207/954
0.87078. 18/0, 342/33.1
FINE
0.847/26.590 340.344
0.79926 88/0 3056.9
0,839/26
368156
O 0.846/26 (00.000002227110 275/7.1
08533/7.32/0.35
FINE+MRINR
0 0002770000.03110 312/7.2
0.839/27 28/0 365/47
0,878/28 40V9 22927.
0.856/27
FINE+SST
0.874/27.36003322
0,86022..520
675/59.1
0,864/28.
MRIN
0.878/27.9002221..
0,825/28 4440 287/29.1
0.862/28 260028009..
0501/30.1500 15/0/19539.3
0.87428.290
2114/28.9000325/13..
NR2N
0.850/26.11M 1150026.1100.34//4. 1/0.3477/4.8
0.79926-9200. 301/7.3
0.835/26 83/0 7741477
0.836/25 09V0 28077.2
0.85027 40/0 362/48
NRIN4MRINR
8.577/6. 180. 345/5.0
0.80266 9000 201/7.6
0.836/66 950 578/5.1
0.57025 5600 242/7.2 6
8384/27 35/0 35W/5
NR2N
0.875/27.490 49/). 323/20.7
0.825/28 2009 283/33.5
0.865/27 S881 263/12.6
(L892) 50022 20776000
0.6477X 2740 343/X_11
MMINRMMIIRSSST
0.87627.600322/133
0.826/88 281128
0.806/88.
210.2///111
0500030 ATW.90007/1119633999
0.87228
336/12.3
SSDU
0.861/25.1660 140.377//777
0.79M22.66M 610 332/7.5
0.818/25
4000 375/52
1090/220350 7300
0.836/24.300
SSDU-MRINK
0.865/5,
0.8018/22.7 100338/77
0.826/24
477777797777
0.953/25
SSDU~SST
387/227.990.133244
0.82M28. 13/0 29142.7
0.860V27.5800
29/12/34
7741/2447110.432990
0.869/28.244 240.343/23.2
SSDU-MRINR+SST
087927.570.32/115
0,22//8.1770.00 17/0.285/3544
1863/281400.28/11.
2001/3025/01192444
0,872/2.30000000 30
Table 10: Performance comparison of UNet methods under in-domain evaluation. Each cell reports
SSIM (t) PSNR (1) / LPIPS (4) / Time (mins/patient) (L). Shaded rows indicate methods that
include the proposed MR-INN--asee adaptation (MRINR) ) and further enhancement via wise
SST refinement ( (MINNR+ST) )
26

---

In-domain Evaluation on VarNet. Table 11 presents comprehensive comparison of VarNet-based reconstruction methods evaluated under in-domain conditions (including DIP-TTT and ZS-SSL). As expected, most methods demonstrate improved performance. Our proposed two-stage adaptation pipeline, incorporating MR-INR and SST, achieves strong results across most datasets terms of SSIM, PSNR, and LPIPS.
Notably, our method (e.g., +MRINR+ attains the best SSIM, PSNR or LPIPS in four of five shifts. An exception occurs in the AXTIPRE + AXTIPRE setting, where baseline+SST achieves slightly better metrics. In contrast, our dual stage approach imposes strong global anatomical prior, which promotes per-slice refinement in this homogeneous setting. A stronger global anatomical prior from MR-INR may slightly limit the flexibility of slice-level adaptation in this shift.
Despite this, our method still delivers highly competitive results with significantly less inference time compared to DIP-TTT. For instance, NR2N+MRINR+SY" achieves comparable PSNR of 28.27 in the T1 case within 18.4 minutes/patient, versus 25.8 minutes for DIP-TTT. This supports the claim that our framework achieves better trade-off's between quality and efficiency, making favorable for real-world applications requiring fast implementation without sacrificing reconstruction accuracy.
Method (VarNet)
Brain
Brain
FastMR
farMRI
AXTIPRE
AXTIPRE
Random
Random
Zoro-filiing
3375 Se9/.
0.247/24.390.9999
0.749/2.7000 35W
0.84026.5200
0,764/25, 8800 3317.
Non-TTT
0.45/24.500 50V0 305/-
0,706/33 220. 3311-
0.838/22 48/0. 3541-
D. 0.14 74/0.580L S80V-
O. 1/15999 5931.
DIP-TTT
0.815/21 211.7/2999..3111 315/102
0.813/28. 26// 282/7.1
0.669/28 2312//2
29,/120.4 0.44029
0.68324 3203332
75-SSI.
0.885/2. 113.111/122444
0.75472.2200 2011222222.7700000 37W 1002
(887627,9330. 334854
0342221 9480, 302/1
0.634/21 4104499
FINE
D. 0.854/36 4907 328/3.
0301/26.558 550 306/7.2 2
0.86//77 7000 335/3.5
0816//4 17,0 273/.4 4
0.646/70 62/0. 388/4.
FINEMMRINR
0.857/26
325(4.7
0,804/6.88
291/7.8
0,85527 4600 343/4.2
0887/2646 225/7.8
0.767/24 4500
FINE+SST
62099100919
329/26.2
204/63.8 0360229
0.697/2A
327/47.1
MINE+MRINR
010
0.22/28. 04655/29.440222200 27922//232
0112228.1600389110
198/44.3
0.787/T
49/022//188
NRIN
8 8686226
0813/26 9510
0,871/27 4300 332/4.3
805/23 3780 28577.6 6
0.64020 76/0, 3884,
NKEN-MRINK
918622265700331955
29088
2.89/27.14K034000
0 2180248/8
NR EREN-SST
1.89022 6900 10.3
0812/27. 7700 288/33.7
0,78/28.55 5500 523/26.8
0838/9 0550 199659.1
0.69K244 MA. 12K448.4
INEEN MRINRASSI
8885/2280/ 306449.7
0326/28 4200 279/22
2467228.7003311118
0344/29 240. 191/45.7
SSDU
0.838/24 690) 344/4.7
0.686/19 0186/19.1200.100 1200.7708.2
0885//2.81100 376//4
0.597/17 4400 36628.1
0.521/17 72/2 421/53
SSDU+MRINR
0,839/24 (900248990.330 8400,34//5
0.713/19.720 350887
0.809/22.8800 18/0.36915.3
0.695/19 9.05//9..22..00 318/8.5
D. 0,563/1 00/0.40//5.4
SSDU4SST
310/12.22
0300/27.770 759:4077
0,871/28.110 1171/28.110033//90044
243/70.5
0.677/33
340441.3
SSDU+RRINR-SST
1.85727-570031050.
0313/28.299.255292
0.6622.200033322..7
0826288820
28922/2
Table 11: Performance comparison of VarNet methods under in-domain evaluation settings. Each cell reports SSIM (t) PSNR (t) LPIPS ()) / Time (mins/patient) (4). Shaded rows indicate methods that include the proposed FRR-IN--asce adaptation (MRINR) ) and further enhancement via slice-wise SST refinement MRINR+SST) )
F Mathematical Analysis for Proposed Method
F1 Test Distribution and Problem Formulation
We consider a setting where the observed signal y is a corrupted version of the underlying clean signal x, which follows the test distribution:
Q:y=x-z, x= -CC++o uQ, c~,N(0,1), 1), 1~)
(12)
Here, U E Raxd is orthonormal basis for the signal subspace, and μo represents the mean shift in the test distribution. Our goal is to estimate x under this distribution shift.
F.2 Self-Supervised Adaptation by Affine Transformation
To address the distribution shift from P to Q, we introduce an adaptation mechanism that accounts for both variance and mean shifts. The optimal estimator for x under test-time training (TTT) is:
x x- + +
(13)
where a accounts for variance shifts, and 3 corrects for mean shifts.
27

---

The self-supervisee loss function is defined as:
2od
Eq [lly aUU -112
-
BQ |I|(T UU*)y (14)
n
Expanding the First Term of Lss:
Be [lly aUU'y -113] =Eq y-yy-2yy'UU' -
to'y'U"'UU" + 20 U (15)
Taking expectation:
2 yy"y] 2aR [y J - 2R [
+a²Ba [y" uu"Uu"y> 2aBo [ Be [3
(16)
Compute Individual Expectations and using expectation properties:
(17)
Since:
Eolyy'} UU + + pQHa. T
(18)
Eqly" y- = +² (((N)H))
(19)
dd+ s² + ||@@||
(20)
For the second expectation:
Boly UU" ((UU'E
(21)
Substituting IEq [yy"):
Eoly" UUTT! y] UU'"
(((UU"(UU" + +MQH))),
(22)
=I((U")) + + I(UU"" (Quz):
(23)
= =d+s'd+u(UU) (QQU))
(24)
Lss(a, B) =
(QuE)) -23 u uotaad+2ad3" +1,811112
(25)
Combine each component, we can get
Lss(a, () = d+ 1l (o d+ | +) +
d 2od nQ - 23 + (26)
Final Simplified Expression for this term
Lss(a, 8) = n + (1 - a) (a² -2a)s2d + 113 - - Holl
(27)
Expending second term:
2ad n
EQ [|| UUT)y
(28)
First, expanding the squared norm:
28

---

[ 00 yyl2 ((1 (1- (I-)
(29)
Since (I- - UU?) is symmetric:
=
(30)
Taking expectation:
Eq ly UU")U">>) tr (aI- Eelly'']) (gll""")
(31)
Using the expectation property:
Bolyy" UU + + PQliQ T
(32)
Substituting:
tr (I- (UU" + + + +QpD))
(33)
Expanding the trace:
tr (1 (1-U))))))))))
(34)
Since (I - UU?) removes the UUT component:
s2 d) ar((I-U)) UU )app)
(35)
Thus, the second term simplifies to:
2ad
| d) + tr ((I UU )o
(36)
n d
Assuming loQ is entirely inside the subspace spanned by U, the projection term vanishes, giving:
20d ( - d).
(37)
Last, we take final simplification Now, simplifying terms:
Lss(a, 8) = s²n +1-a))d++ (a² - 2a)ssdd ||3 p2ll 2ads
(38)
Combining the 2d terms:
(a² - 2d d adddd 2ns + 2as = =
(39)
Thus, the final loss function simplifies to:
3) =
-
(40)
Finally, compute the derivatives For derivative with Respect to a
ØLss
-2d(1 a)) + 2ads"
(41)
da
29

---

Setting this to zero and solving for a":
a'
(42)
1 82
For derivative with respect to 8
0Lss
= 2(3 - HQQ.
(43)
03
Setting this to zero and solving for 8*:
8 uQ.
(44)
In conclusion,
1. a" dynamically adjusts for noise variance shifts.
2. 3* corrects for mean shifts, making adaptation robust in OOD settings.
G Supplementary Visualisations
While the main paper presents qualitative comparisons on UNet (FINE) under the anatomy shift, this appendix includes additional visualisations across the remaining domain shifts. We provide side-by- side comparisons of reconstruction results for our method and competing approaches, including DIP. TTT and ZS-SSL. Notably, ZS-SSL results are visualised under the VarNet backbone originally proposed with data consisteney block. Our visualisations offer more comprehensive view of cross-domain performance across architectures and adaptation strategies.
G.1 UNet
Comunc-Truth
Zam=llling
Na--TTA
SI--TTA
FIME
NE MRIMM
FNF HETT
Our
Figure 9: Comparison of different frameworks in UNet under dataset shift (Stanford to fastMRI) using the FINE method. The first shows reconstructed MRI images, while the second row presents residual maps between reconstructions and full-sampled MRI.
30

---

Ground-Trth
Zero-iling
Non-TTA
DIP-TTA
FINE
FINE-MRINR
FINE-SST
Our
Figure 10: Comparison different frameworks UNet under modality shift (AXT2 to AXTIPRE using the FINE method. The first shows reconstructed MRI images, while the second row presents residual maps between reconstructions and full-sampled MRI.
Ground-Truth
Zero-lling
Non-TTA
DIP-TTA
FINE
FINE+WRIN
FINE+BST
Our
Figure 11: Comparison of different frameworks in UNet under acceleration shift (2X to 4X) using the FINE method. The first shows reconstructed MRT images, while the second row presents residual maps between reconstructions and full-sampled MRI.
Gmund-Trathh
Zam--ling
Ner-TTA
DI-ITA
FINI
FNE-MRINR
FINE-SST
Figure 12: Comparison of different frameworks in UNet under sampling shift (random to uniform) using the FINE method. The first row shows reconstructed MRI images, while the second row presents residual maps between reconstructions and full-sampled MRI.
31

---

G.2 VarNet
Figure 13: Comparison of different frameworks in VarNet under anatomy shift (Knee Brain) using the FINE method. The first row shows reconstructed MRI images, while the second row presents residual maps between reconstructions and full-sampled MRI.
TrouhshTruth
2ero
Nas
DP--TA
28-88L
FINE
FRNEWRIN
FNE
Figure 14: Comparison of different frameworks in VarNet under dataset shift (Stanford to fastMRI) using the FINE method. The first row shows reconstructed MRI images, while the second row presents residual maps between reconstructions and full- full-sampled MRI. The proposed method (far right) achieves the lowest residuals, indicating improved reconstruction accuracy
Treand-Trch
Zetiiliigg
Non-TT
DI--TT
23 SBL
FNEE
FNEHWAIR
FNEE
Figure 15: Comparison of different frameworks VarNet under modality shift (AXT2 AXTIPRE) using the FINE method. The first row shows reconstructed MRI images, while the second row presents residual maps between reconstructions and full-sampled MRI.
Ground Trudh
Zorofling
Nas-TA
OP-TAA
28-83L
FINE
RINEWBIIN
FINE-SST
Our
Figure 16: Comparison of different frameworks in Varnet under acceleration shift (2X 4X) using the FINE method. The first row shows reconstructed MRI images, while the second row presents residual maps between reconstructions and full-sampled MRI.
32

---

Ground-Tech
Zero-Bling
Nee-TTA
DIN-TA
25-65L
TNE
FRE-VENR
TIE-EST
OuT
Figure 17: Comparison of different frameworks in VarNet under sampling shift (random to uniform) using the FINE method. The first row shows reconstructed MRI images, while the second row presents residual maps between reconstructions and full- full-sampled MRI.
33


Reviews:
[{"review_id": "yPGXMQgUfp", "reviewer": "Reviewer_5sGP", "summary": "The authors propose a dual-stage test-time adaptation framework for fMRI reconstruction in the compressed sensing domain. The first stage is to adapt a model trained on one domain to a new patient more generally, and the second refines the model to the individual slices of that patient. Ablation studies and results across five datasets indicate that the each of the authors' stages and modules contributes to performance improvements in terms of SSIM and PSNR.", "questions": "As mentioned in the strengths and weaknesses section, I think the following questions are important to answer:\n1. Why are the ablations purely done on the U-Net architecture when both architectures were used in the paper?\n2. Why did the authors choose SIREN when the paper they cite seems to imply that other architectures could have been better choices?\n3. Are the results significant?", "limitations": "Yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 1, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths**\\\nI think the authors introduce original modifications to the field of test-time adaptation, I like the idea of separating out the patient adaptation and single-slice refinement. Moreover, the authors' results seem to indicate a significant improvement over previous works, although I would think it strengthens the work even more if the authors actually performed significance tests for their results. Especially compared to DIP-TTT, some of the results come close, and it is unclear whether these results are significant. All-in-all, I think this work can be a significant contribution to the field if the authors address the issues below in their rebuttal.\n\n**Major weaknesses**\\\nI think the major weakness for this paper is that the quality and clarity need to be significantly improved before I can recommend this paper for acceptance. The introduction of the method is quite unclear, and I found it hard to follow exactly how all of the authors' improvements fit together into a larger framework. Specifically, the explanation of the AD module and section 4.2&4.3 are unclear. An example of an unclear paragraph are lines 124-128. Moreover, this extends to Figure 4, which is incredibly hard to read, is badly formatted, and I can therefore not verify their U-Net results. It is also unclear to me why the results are presented differently for the VarNet (table 2) and U-net architecture (Figure 4). Moreover, why are the ablations purely done on the U-Net architecture when both architectures were used in the paper?\n\n**Minor weaknesses**\\\nThe authors cite the following paper: \"Among various designs [15], SIREN remains a strong choice ...\". However, in the paper that the authors refer to, the discussion states the following:\n\"For applications where computational efficiency is less critical and the highest reconstruction quality is\nneeded, Incode would be the preferred choice. However, for real-time applications or cases where a balance\nbetween quality and speed is crucial, Fr and Finer offer strong alternatives with their adaptable frequency\nhandling and more manageable computation times. Siren can be a good option when tasks require periodic\nsignal reconstruction but with less variability in frequency content. One area where INR methods still face\nchallenges is scalability, particularly in handling extremely high-resolution or highly detailed tasks. Future\nwork could explore more efficient frequency encoding mechanisms that reduce the computational overhead\nwithout sacrificing quality. Additionally, optimising activation functions to be more adaptive to task-specific\nrequirements could improve generalisation across diverse datasets and applications. Enhancing the dynamic\nadaptability of models like Finer could allow for more robust performance across tasks that involve varying\nlevels of detail, potentially improving their usability in real-world scenarios.\"\nIt seems like INCODE, Fr, and Finer are potentially better backbone models for this specific task because I am unsure why we would expect more periodic signal reconstruction, but less variability in the frequency content. Moreover, in their paper, (Table 2), the medical imaging results indicate that Fr would be a much better choice. Can the authors comment on this or potentially perform an ablation study to test these effects?\n\n**Spelling/grammar**\\\nL3: \"... this discrepancies ...\" -> these \\\nL15-16: \"... can integrate well with various self-supervised (SSL) framework, ...\" -> frameworks \\\nL126: \"... and Fourier feature ...\" -> features \\\nL138: \"... before last layer ...\" -> the last layer \\\nL166: \"... given an set of feature u, ...\" -> given a set of features u \\\nL181: \"In calculation of AD equation ...\" -> the AD equation", "was_revised": true, "final_justification": "The authors have generally been able to address my concerns in their rebuttal, it is hard to verify that they have improved their figures, and exactly how much better they explain their method, but I believe (given the examples of improved writing they give in their rebuttal) that the authors will be able to make the changes that I find important before recommending this paper for publication. Given that I can't fully assess the above, I decided to increase my score to a 4.", "rebuttal": "We sincerely thank the reviewer for the detailed and constructive feedback. Your comments have greatly helped us identify key areas for the clarification of our method and results. For the spelling/grammar error, we will correct them in final version. Below, we address your main concerns.\n\nQ1: Clarity Concerns\n\nIn the Introduction (Lines 47–70) and the beginning of Section 3 (Method), we summarize the motivation and high-level design of D2SA, highlighting its two-stage structure:\n\nStage 1: Patient-wise Distribution Adaptation – We use an MR-specific Implicit Neural Representation (MR-INR) to model shared representations across slices. Each slice’s coordinates are extended with a patient-specific latent code (z_p) and random Fourier features to stabilize convergence and express frequency shifts. These inputs are passed through a SIREN network to learn mean/variance modulation parameters (α,β), allowing distribution alignment for all slices in a patient.\n\nStage 2: Slice-wise Structural Refinement – For each slice, we freeze the encoder and patient latent code and fine-tune only the INR decoder and a lightweight, learnable Anisotropic Diffusion (AD) module. The AD module extracts directional gradients using difference convolutions (see Line 171–180) and generates adaptive edge-aware refinement weights.\n\nDetails of the AD module in Section 4.2&4.3: Regarding Section 4.2, due to space constraints, we initially omitted the explicit formulation of the five directional difference convolutions used to estimate gradient-aware anisotropic diffusion coefficients. These convolutions extract directional derivatives (horizontal, vertical, diagonal, etc.) with end-to-end learning machanism. For example, taking the Horizontal Difference Convolution (HDC) as a case: the horizontal gradient is first computed via differences between pixel pairs along the x-axis. After training, the learned kernel weights are re-arranged and applied directly as convolution filters on the input feature map. These filters exhibit properties similar to handcrafted operators (e.g., their horizontal weights sum to zero), enabling structural-aware modulation. We will briefly summarize this process in the main paper. For Section 4.3, the theoretical derivation of the LSS-based optimization is given in Appendix Section 5; we will highlight this in the main text.\n\nClarifying Lines 124–128: We rephrase it as follows for better clarity: “Following patient-level batch training, each slice is associated with a latent identity code. In the MR-INR branch, this latent code is concatenated with Fourier-encoded spatial coordinates before being passed to a SIREN network. This combination enhances convergence and representation power by encoding slice-specific anatomical priors and capturing periodic signals in MRI signal acquisition.”\n\nFigure 4 and UNet result：To avoid table overcrowding and emphasize key trends, we visualized UNet results as charts. These highlight that: (i) MR-INR provides the largest PSNR gain under modality shift (top-left); (ii) our full method outperforms baselines with lower LPIPS and faster inference (bottom-left); (iii) MR-INR and SST consistently improve SSIM across all domain shifts (right). Full UNet tables are in Appendix Table 1, and VarNet charts in Appendix Fig. 1. We will move UNet table to main page and keep all charts in Appendix in the final version.\n\n\nQ2: Ablation studies on VarNet\n\nWe extend the full-stage ablations to VarNet under the anatomy shift setting, including additional baselines including SST-only+AD and FINE+SST+AD. The VarNet part will be added into final version.                      \n\n| MR-INR / SST Ablation (VarNet)                                        | PSNR ↑ | Params ↓ | Time ↓ |\n|------------------------------------------------|--------|-----------|--------|\n| Patient-wise training                          |        |           |        |\n| FINE                                           | 24.01  | 29.45     | 3.9    |\n| +MR-INR (🧊 latent)                             | 26.37  | 29.69     | 4.7    |\n| +MR-INR (🔥 latent)                             | 26.45  | 29.69     | 5.0    |\n| Single-slice training without stage 1          |        |           |        |\n| SST (🧊 CNN + 🔥 AD)                             | 27.50  | 16.74     | 56.8   |\n| Single-slice training with stage 1             |        |           |        |\n| FINE + SST (🔥 CNN)                             | 27.57  | 29.45     | 53.6   |\n| FINE + SST (🧊 CNN + 🔥 AD)                      | 27.58  | 16.74     | 53.3   |\n| MR-INR + SST (🔥 CNN)                           | 27.68  | 29.69     | 20.9   |\n| MR-INR + SST (🔥 CNN + 🔥 AD)                   | 27.61  | 43.79     | 34.0   |\n| MR-INR🧊 + SST (🧊 CNN + 🔥 AD)                  | 27.63  | 16.74     | 27.8   |\n| MR-INR + SST (🧊 CNN)                           | 27.45  | **2.88**  | 21.6   |\n| MR-INR + SST (🧊 CNN + 🔥 AD) (**Ours**)        | **27.68** | 16.98 | **17.1** |\n\nThe extended ablation study highlights the functional contributions and trade-offs of each D2SA component across VarNet backbones. We observe that Stage 2 (SST+AD) with/without stage1 training offer reasonable performance, but at the cost of significantly higher inference time (~50–56 mins per patient). Incorporating Stage 1 (MR-INR) leads to stronger initialization for slice-wise refinement, reducing convergence time substantially (up to 3× faster inference) and yielding consistent performance gains. Notably, our final configuration (MR-INR (🧊 latent) + SST (🧊 CNN + 🔥 AD) achieves the best PSNR while maintaining low parameter count and the fastest inference time (e.g., 17.1 min/patient for VarNet). These results validate our core claim: D2SA’s staged modularity is not only conceptually sound, but also practically effective, enabling scalable, fast, and adaptive inference with minimal tuning. Each module remains plug-and-play, ensuring generalizability and ease of adoption in various architectures and deployment scenarios.\n\nQ3:Choice of SIREN over Other INRs\n\nTo clarify our choice of SIREN as the INR backbone in MR-INR, we conducted an additional ablation comparing different INR backbones under both patient-wise (FINE+MR-INR) and single-slice (FINE+MR-INR+SST) training. Results are summarized below:\n\n| Stage 1 | Stage 1 (SSIM↑ / PSNR↑ / LPIPS↓) | Stage1 + Stage 2 | Stage 2 (SSIM↑ / PSNR↑ / LPIPS↓) |\n| :--- | :--- | :--- | :--- |\n| WIRE | 0.839 / 25.78 / 0.354 | Finer | 0.873 / 27.40 / 0.323 |\n| Finer | 0.845 / 26.05 / 0.350 | WIRE | 0.872 / 27.44 / 0.321 |\n| Random PE + MLP | 0.845 / 25.76 / 0.349 | Random PE + MLP | 0.864 / 27.22 / 0.326 |\n| Only SIREN | 0.845 / 26.16 / 0.349 | Only SIREN | 0.874 / 27.51 / 0.322 |\n| **Ours (PE + SIREN)** | **0.845 / 26.37 / 0.346** | **Ours (PE + SIREN)** | **0.876 / 27.71 / 0.320** |\n\nOur design combining random Fourier positional encoding with SIREN consistently yields the best or near-best performance, especially in perceptual quality (LPIPS). While Finer offers frequency adaptability, its more complex architecture increases overhead without clear performance gains; WIRE, though efficient, suffers from unstable convergence and limited representation in medical shift settings. Compared to INCODE, our SIREN-based MR-INR avoids the need for pretraining, supporting our lightweight, plug-and-play adaptation objective.\n\nWe will include these results in the final paper. \n\nQ4:Result Significance and Efficiency\n\nWe thank the reviewer for the helpful suggestion. We would like to clarify statistical significance tests are already included in Supplementary Figure 8, where we compare our method (SSDU+MR-INR+SST) with DIP-TTT and +SST using Wilcoxon signed-rank tests. Under UNet (acceleration shift) and VarNet (sampling shift), we observe significant improvements in all metrics (p value < 0.05).\n\nWe also would like to highlight efficiency gains, even in cases with close average scores. For example:\n\nIn VarNet on anatomy shift (Table 1), our method improves SSIM from 0.878 → 0.882 and PSNR from 27.67 → 27.68, while reducing inference time from 52.5 min to 17.1 min, a 67% reduction.\n\nIn U-Net on sampling shift (Table 3), our method achieves LPIPS 0.311 vs. 0.314 (DIP-TTT) with 13.2 min vs. 27.1 min, yielding a>50% faster adaptation while maintaining superior quality."}, {"review_id": "SHyDNyFz2O", "reviewer": "Reviewer_SZTm", "summary": "The paper proposes a dual-stage Test-Time Adaptation (TTA) method (D2SA) to address domain shifts in MRI reconstruction.\n\nStage 1 (distribution-level adaptation) uses MRI implicit neural representations (MR-INR) to adapt to patient-specific distribution shifts.\n\nStage 2 (slice-level adaptation) employs anisotropic diffusion modules to refine reconstructions at the slice level, preserving structural fidelity.\n\nIt demonstrates consistent improvements across various MRI distribution shifts (anatomy, modality, dataset, sampling, and acceleration).", "questions": "Can the authors clarify explicitly what distinguishes their method fundamentally from existing slice-wise refinement or TTA methods, beyond merely combining MR-INR and anisotropic diffusion?\n\nHow sensitive is the method to hyperparameter choices such as latent code dimensionality or anisotropic diffusion parameters?", "limitations": "yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n**Good experimental validation**\n\nThe paper presents extensive quantitative evaluations under multiple distribution shifts, demonstrating performance improvements. Visual results provided in the appendix are convincing and clearly show the effectiveness of the proposed method in comparison to existing baselines like DIP-TTT and ZS-SSL.\n\n**Effective combination of existing techniques**\nIntegrates Implicit Neural Representations (INR) and anisotropic diffusion, both proven techniques, to enhance reconstruction performance and efficiency. It achieves notable efficiency improvements (reduced adaptation time compared to ZS-SSL and DIP-TTT), making the method practical for real-world scenarios.\n\n\nWeakness \n\nx. The authors acknowledge inspirations from existing works (e.g., DIP-TTT, Functa, and SSDU), but the paper could explicitly discuss the novelty more clearly, especially distinguishing from recent diffusion-based approaches. \n\nx. The authors introduce an additional layer of complexity by using the INR framework to handle patient-level distribution adaptation.\nHowever, INR requires careful hyperparameter tuning (latent vector size, network depth, initialization) to avoid instability issues. Hence, a clearer analysis of hyperparameter sensitivity and computational complexity could improve transparency and could help understand the practical implications of this complexity better.", "was_revised": true, "final_justification": "Technique-wise, this paper sounds reasonable to me.", "rebuttal": "We thank the reviewer for the thoughtful suggestions. Your recognition of our dual-stage framework’s effectiveness and efficiency is greatly appreciated. Below, we address your comments regarding the clarity of architectural differences, the distinctions from diffusion-based test-time adaptation methods, and hyperparameter sensitivity.\n\nQ1: Architectural Differences\n\nBeyond architectural differences, our two-stage D2SA framework is designed with realistic clinical deployment in mind, where direct zero-shot transfer or pure slice-wise refinement often fails to provide reliable reconstructions—especially under large distribution shifts. This unreliability can directly impact early-stage screening and the localization of small or subtle lesions.\n\nIn clinical scenarios, radiologists often need initial high-quality reconstructions across all slices for efficient review, followed by selective refinement on suspicious or diagnostically relevant slices.\n\nTo this end:\n\nStage 1 (MR-INR) performs a fast, patient-level adaptation, leveraging inter-slice structure to learn global distributional shifts (mean, variance). It provides a reliable reconstruction baseline within ~5–7 minutes, without requiring slice-wise optimization.\n\nStage 2 (SST + AD module) then allows targeted refinement on demand, enhancing structural fidelity on specific slices without re-training the full network. The AD module preserves fine-grained anatomical details (e.g., tissue boundaries), which are often over-smoothed by conventional TTA methods.\n\nEach component is deliberately positioned:\n\nMR-INR enables compact patient-specific modeling, aligned with the notion of shared anatomical priors.\n\nAffine adaptation (α, β) efficiently compensates for patient-specific mean/variance shifts with provable benefits (Section 4.3).\n\nThe AD module, integrated into SST, provides structure-aware filtering under frozen CNNs, striking a balance between efficiency and precision.\n\nQ2: The distinctions from diffusion-based test-time adaptation methods\n\nUnlike diffusion-based TTA approaches that require heavy pretraining and offer limited flexibility, our method is pluggable, interpretable, and clinically actionable. This hierarchical strategy is not merely a module combination but a functionally structured design tailored for practical, slice-selective, low-resource test-time adaptation in real-world medical workflows.\n\nQ3: Sensitivity about hyperparameter on latent code and AD\n\nTo clarify robustness of our INR-based adaptation, we show additional sensitivity experiments on three critical hyperparameters: latent code size, INR network depth, and latent code initialization scale. As shown below, our method exhibits stable performance across a wide range of values:\n\n| TTA Stage   | Variant                           | SSIM↑                  | PSNR↑                  | LPIPS↓                 |\n| ----------- | --------------------------------- | --------------------- | --------------------- | --------------------- |\n| **Stage 1** | Latent Code Size (64 / **128** / 256) | 0.849 / 0.845 / 0.850 | 26.39 / 26.37 / 26.47 | 0.345 / 0.346 / 0.335 |\n|             | INR Depth (3 / **4** / 5)             | 0.842 / 0.845 / 0.848 | 26.34 / 26.37 / 26.44 | 0.345 / 0.346 / 0.346 |\n|             | Init Std (0.1 / **0.01** / 0.001)     | 0.845 / 0.845 / 0.847 | 26.50 / 26.37 / 26.37 | 0.346 / 0.346 / 0.345 |\n| **Stage 2** | Latent Code Size (64 / **128** / 256) | 0.876 / 0.876 / 0.877 | 27.53 / 27.71 / 27.53 | 0.323 / 0.320 / 0.320 |\n|             | INR Depth (3 / **4** / 5)             | 0.874 / 0.876 / 0.877 | 27.54 / 27.71 / 27.56 | 0.321 / 0.320 / 0.319 |\n|             | Init Std (0.1 / **0.01** / 0.001)     | 0.876 / 0.876 / 0.875 | 27.53 / 27.71 / 27.52 | 0.321 / 0.320 / 0.322 |\n\nOur default configuration (highlighted in bold: 128-d latent code, depth 4, init std 0.01) achieves a strong trade-off between stability and performance. Performance is consistent across hyperparameter ranges, with differences ≤ 0.02 PSNR or ≤ 0.01 LPIPS. This suggests our method is not overly sensitive and avoids instability even with pluggable configurations. The default setup ensures robust adaptation without excessive tuning overhead.\n\nMoreover, to show the robustness of our method to the anisotropic diffusion (AD) step size, we conducted ablation experiments under modality shift (UNet with FINE backbone). As shown below, varying the AD step size from 1.0 to 0.01 leads to minimal changes in performance:\n\n| AD Step Size | PSNR ↑    | SSIM ↑    | LPIPS ↓   |\n| ------------ | --------- | --------- | --------- |\n| **1.0**      | **27.71** | **0.876** | **0.320** |\n| 0.1          | 27.38     | 0.874     | 0.322     |\n| 0.01         | 27.36     | 0.874     | 0.323     |\n\nThese results demonstrate that our method is robust to the choice of the diffusion step size, with less than 0.4 dB PSNR fluctuation and negligible variation in perceptual quality. The default choice of step=1.0 achieves the best trade-off between sharpness and stability."}, {"review_id": "rXzZNsLKAj", "reviewer": "Reviewer_rEsT", "summary": "This paper proposes D2SA, a two-stage test-time adaptation (TTA) framework for MRI reconstruction. The goal is to improve model performance when faced with distribution shifts between training and testing data. The method first employs a patient-wise adaptation stage using an MRI-specific Implicit Neural Representation (MR-INR) to capture global mean and variance shifts for a given patient. This is followed by a second stage that performs single-slice refinement. This refinement stage freezes most of the base network and the learned patient-level latent code for efficiency while fine-tuning the MR-INR and a novel, learnable Anisotropic Diffusion (AD) module to preserve structural details. The authors evaluate D2SA across five simulated domain shift scenarios, showing consistent performance improvements over several TTA baselines.", "questions": "1. The core of the paper is the two-stage design. Could you provide an ablation study that compares a simpler baseline (e.g., FINE) directly with that same baseline enhanced only by Stage 2 (i.e., FINE+SST+AD)? This would help clarify whether the complex Stage 1 patient-wise adaptation is truly necessary or if most of the benefit comes from the powerful slice-refinement stage alone.\n2. The proposed system involves numerous components and corresponding hyperparameters (e.g., loss weights λ_self, λ_INR, λ_reg; latent code variance σ, etc.). The paper does not discuss the sensitivity of the results to these choices. How robust is D2SA to variations in these hyperparameters? A brief analysis would be crucial for assessing the method's practical usability and reproducibility.\nComputational Overhead vs. Gain: While adaptation time is reported, what is the increase in parameter count and computational complexity (e.g., FLOPs) of the D2SA framework compared to a baseline like FINE? A more direct comparison would help readers assess if the marginal performance gains in some scenarios justify the added model and computational complexity", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strengths\n1. The paper addresses the highly relevant and practical problem of domain shifts in medical imaging, which is a significant barrier to the real-world deployment of deep learning models.\n2. The experimental setup is a clear strength. The authors have commendably evaluated their method across five different, well-motivated domain shift scenarios and against a suite of relevant TTA baselines.\n3. The paper is well-structured and generally easy to read. The figures, particularly Figure 1 and Figure 2, effectively communicate the core concepts and the architecture of the proposed framework.\n\nWeaknesses\n1. The primary weakness is that the D2SA framework, while elaborate, appears to be a complex combination of several known techniques. Implicit Neural Representations (INRs), test-time feature modulation, self-supervised losses, and anisotropic diffusion are all existing concepts. While their combination is novel, the paper lacks a core conceptual breakthrough. The contribution feels more like a sophisticated engineering effort than a fundamental advance. The complexity of this multi-stage, multi-component system is very high, which may act as a barrier to adoption.\n2. Due to the method's complexity, it is difficult to ascertain the primary drivers of the performance improvement. While the ablation studies are helpful, they don't fully disentangle the contributions. For example, the visual improvements shown in Figure 5 are attributed to the full \"Our\" method (FINE+MR-INR+SST+AD). It is unclear how much of this improvement is simply due to the powerful SST+AD refinement stage, versus the full two-stage pipeline. This makes it hard to judge the true value of the patient-wise adaptation stage.", "was_revised": true, "final_justification": "The authors have addressed most of my concerns, but it remains necessary to discuss their innovativeness from a methodological perspective. Therefore, I consider a score of 4 to be reasonable. If forced to choose between acceptance and rejection, I believe the paper can be published.", "rebuttal": "We sincerely thank the reviewer for the detailed summary and constructive comments. We appreciate your recognition of the practical value of our framework, the clarity of our experimental design, and the relevance of addressing domain shifts in medical imaging. Below, we respond to your main concerns regarding the framework, component contributions, hyperparameter sensitivity, and computational overhead, and we provide additional analyses to address the concerns.\n\nQ1:The Method’s Complexity and the Use of Known Components\n\nConceptual contributions in adapting INR for test-time domain shift: To the best of our knowledge, INRs have not been previously used in test-time adaptation for image reconstruction. We leverage the compact functional expressiveness of INR to learn a new patient-specific representation at test time, not to generate images, but to guide the adaptation of source models in a structure-aware way. This is conceptually distinct from both conventional pretraining-based INR usage (e.g., Functa) and standard slice-wise TTA.\n\nUnified modular architecture with pluggable design: Each component (MR-INR, affine modulation, SST refinement, and AD module) is designed to be lightweight, interchangeable, and orthogonal. This enhances not only performance, but also flexibility and practical adoption. For example:\n\nIf compute is limited, users can skip Stage 2 and rely on Stage 1 alone.\n\nIf specific slices are flagged by clinicians, only Stage 2 is applied.\n\nA holistic test-time design perspective: Our framework proposes a structured pipeline that mimics how real clinical workflows operate—first broadly adapting to the patient, then selectively refining critical regions. This hierarchical control is not present in prior works and reflects a pragmatic yet theoretically motivated design.\n\nWhile we do build on existing components, our architectural integration and adaptation strategy are novel, practical, and aligned with real-world test-time usage constraints—thus providing both scientific insight and engineering utility.\n\nQ2:Necessity of Stage 1: Is most benefit from Stage 2?\n\nWe provide a detailed ablation comparing three configurations on both UNet and VarNet under anatomy shift, including Stage 2 only (FINE + SST + AD); Stage 1 + Stage 2 without MR-INR (FINE + SST + AD but with pretrained encoder from FINE) and Full D2SA (FINE + MR-INR + SST + AD).\n\n| Configuration (UNet)                           | PSNR ↑    | Params (M) ↓ | Time (min/patient) ↓ |\n| ---------------------------------------- | --------- | ------------ | -------------------- |\n| Stage 2 only (FINE + SST + AD)           | 27.31     | 17.62        | 18.7                 |\n| Stage 1 + 2 w/o MR-INR (FINE + SST + AD) | 27.37     | 17.62        | 22.6                 |\n| **Full D2SA**                            | **27.71** | 17.89        | **12.1**             |\n\n| Configuration  (VarNet)                          | PSNR ↑    | Params (M) ↓ | Time (min/patient) ↓ |\n| ---------------------------------------- | --------- | ------------ | -------------------- |\n| Stage 2 only (FINE + SST + AD)           | 27.50     | 16.74        | 56.8                 |\n| Stage 1 + 2 w/o MR-INR (FINE + SST + AD) | 27.58     | 16.74        | 53.3                 |\n| **Full D2SA**                            | **27.68** | 16.98        | **17.1**             |\n\nCompared to Stage 2 only (FINE+SST+AD), which uses only FINE features, our Full D2SA introduces the Stage 1 (MR-INR) and consistently boosts PSNR by 0.18~0.4 dB More importantly, inference time is reduced by >30% (UNet) and nearly 3× (VarNet) when MR-INR provides better initialization for SST. This shows that Stage 1 is not redundant: it not only improves image quality but also accelerates slice-level optimization in Stage 2, especially combining MR-INR in the stage 1.\n\nQ3: Hyperparameter sensitivity\n\nTo further support the robustness of our method in hyperparameters settings, we show the dedicated robustness results on the key hyperparameters in both Stage 1 (MR-INR) and Stage 2 (SST+AD), including: Latent code size (64 / 128 / 256)；INR network depth (3 / 4 / 5)；Latent code initialization std (0.1 / 0.01 / 0.001)\n\n| TTA Stage   | Variant                           | SSIM↑                  | PSNR↑                  | LPIPS↓                 |\n| ----------- | --------------------------------- | --------------------- | --------------------- | --------------------- |\n| **Stage 1** | Latent Code Size (64 / **128** / 256) | 0.849 / 0.845 / 0.850 | 26.39 / 26.37 / 26.47 | 0.345 / 0.346 / 0.335 |\n|             | INR Depth (3 / **4** / 5)             | 0.842 / 0.845 / 0.848 | 26.34 / 26.37 / 26.44 | 0.345 / 0.346 / 0.346 |\n|             | Init Std (0.1 / **0.01** / 0.001)     | 0.845 / 0.845 / 0.847 | 26.50 / 26.37 / 26.37 | 0.346 / 0.346 / 0.345 |\n| **Stage 2** | Latent Code Size (64 / **128** / 256) | 0.876 / 0.876 / 0.877 | 27.53 / 27.71 / 27.53 | 0.323 / 0.320 / 0.320 |\n|             | INR Depth (3 / **4** / 5)             | 0.874 / 0.876 / 0.877 | 27.54 / 27.71 / 27.56 | 0.321 / 0.320 / 0.319 |\n|             | Init Std (0.1 / **0.01** / 0.001)     | 0.876 / 0.876 / 0.875 | 27.53 / 27.71 / 27.52 | 0.321 / 0.320 / 0.322 |\n\nAs shown above, the performance across PSNR / SSIM / LPIPS remains stable, with <0.15 dB variation in PSNR and negligible impact on LPIPS.\n\nWe also show the results about different combinations of loss weights for Stage 1: λ_Self / λ_INR / λ_Reg; Stage 2: λ_Self / λ_INR.\n\n| Stage   | λ Settings     | PSNR ↑ | SSIM ↑ | LPIPS ↓ |\n| ------- | -------------- | ------ | ------ | ------- |\n| Stage 1 | 1 / 1 / 1e-4   | 24.97  | 0.832  | 0.385   |\n|         | 1 / 0.1 / 1e-4 | 23.85  | 0.823  | 0.386   |\n|         | 1 / 1 / 0.1    | 24.00  | 0.822  | 0.388   |\n| Stage 2 | 1 / 1          | 28.04  | 0.860  | 0.287   |\n|         | 1 / 0.1        | 28.00  | 0.861  | 0.356   |\n|         | 1 / 0.01       | 27.99  | 0.861  | 0.350   |\n\nWe used empirically chosen default settings (Stage 1: λ = (1, 1, 1e-4); Stage 2: λ = (1, 1)). The results remain stable across a range of values, indicating good robustness of our framework. However, we observe that setting λ_INR too low (e.g., 0.1) leads to performance degradation, particularly in Stage 1 and LPIPS in stage 2. This is expected, as MR-INR plays a central role in modeling patient-level distribution shifts. A sufficiently weighted INR loss encourages better representation learning of domain-specific patterns, which is crucial for boosting TTA effectiveness.\n\n\nQ4:Computational Overhead vs. Gain: \n\nWhile our method does introduce additional modules (INR and AD), we would like to clarify that we design the D2SA with practical efficiency and controllability in mind:\n\nFrozen base networks reduce trainable parameters: Unlike methods like FINE that update all weights, our approach freezes the base CNN (U-Net/VarNet), and only updates light-weight modules (MR-INR, affine modulation, AD), leading to significantly fewer trainable parameters. This is evident in Table 2, where D2SA consistently requires fewer parameters than full-model tuning.\n\nStage-wise adaptation reduces convergence time: Although D2SA has more components, it achieves faster and more stable convergence. As shown in Figure 4 (main) and Figure 7 (supplement), inference time is reduced at least 60% compared to FINE+SST or DIP-TTT under the same early stopping setup.\n\nEfficient initialization for refinement: Importantly, Stage 1 acts as a structured, patient-aware initialization for Stage 2, providing prior distribution alignment and faster convergence for slice-level refinement. This makes Stage 2 more effective and efficient, especially for structurally important slices.\n\nIn summary, D2SA offers a favorable trade-off: while FLOPs do increase, our design leads to lower parameter counts, faster convergence, and more robust reconstructions, making it more practical for clinical deployment than existing monolithic TTA approaches."}]

Author rebuttal:

Meta-review: This paper proposes D2SA, a dual-stage test-time adaptation framework for MRI reconstruction, designed to improve robustness under distribution shifts. The method is evaluated across five scenarios: anatomy, modality, acceleration, SNR, and sampling, showing consistent gains over existing TTA baselines.
Reviewers highlighted key strengths, including the clinical importance of tackling domain shifts, the comprehensive experimental evaluation, and the clear presentation. At the same time, they noted that the contribution feels incremental as it combines existing components. There was also a concern about the complexity of the framework, and it was initially unclear which elements drive the improvements or how robust the method is to hyperparameters and overhead.
The rebuttal provided clarifications, with additional ablations, robustness analyses, and efficiency results that helped address concerns about necessity, stability, and practicality.
Overall, while the conceptual novelty remains limited, the work is technically solid, carefully validated, and practically relevant. The reviewers and myself  consider this a reasonable accept.
Decision: Accept (poster)