Fast MRI for All: Bridging Access Gaps by Training without Raw Data
Authors: Yasar Utku Alcalar
Merve Gulle
Mehmet Akcakaya
Venue: NeurIPS 2025 spotlight ()
Keywords: Computational Imaging
Fast MRI
Unsupervised Learning
Compressed Sensing
Deep Learning
Access
Primary area: machine_learning_for_sciences
TL;DR: Training PD-DL reconstruction from routine clinical images without raw data to improve fast MRI access

Abstract: Physics-driven deep learning (PD-DL) approaches have become popular for improved reconstruction of fast magnetic resonance imaging (MRI) scans. Though PD-DL offers higher acceleration rates than existing clinical fast MRI techniques, their use has been limited outside specialized MRI centers. A key challenge is generalization to rare pathologies or different populations, noted in multiple studies, with fine-tuning on target populations suggested for improvement. However, current approaches for PD-DL training require access to raw k-space measurements, which is typically only available at specialized MRI centers that have research agreements for such data access. This is especially an issue for rural and under-resourced areas, where commercial MRI scanners only provide access to a final reconstructed image. To tackle these challenges, we propose Compressibility-inspired Unsupervised Learning via Parallel Imaging Fidelity (CUPID) for high-quality PD-DL training using only routine clinical reconstructed images exported from an MRI scanner. CUPID evaluates output quality with a compressibility-based approach while ensuring that the output stays consistent with the clinical parallel imaging reconstruction through well-designed perturbations. Our results show CUPID achieves similar quality to established PD-DL training that requires k-space data while outperforming compressed sensing (CS) and diffusion-based generative methods. We further demonstrate its effectiveness in a zero-shot training setup for retrospectively and prospectively sub-sampled acquisitions, attesting to its minimal training burden. As an approach that radically deviates from existing strategies, CUPID presents an opportunity to provide broader access to fast MRI for remote and rural populations in an attempt to reduce the obstacles associated with this expensive imaging modality. Code is available at https://github.com/ualcalar17/CUPID.

Fast MRI for All: Bridging Access Gaps by Training without Raw Data
Yaşar Utku Alçalar University of Minnesota alca1029@um, edu
Merve Gülle University of Minnesota glle0001 @umn. edu
Mehmet Akçakaya" University of Minnesota akcakaya@umn. edu
Abstract
Physics-driven deep learning (PD-DL) approaches have become popular for im- proved reconstruction of fast magnetic resonance imaging (MRI) scans. Though PD-DL offers higher acceleration rates than existing clinical fast MRI techniques, their use has been limited outside specialized MRI centers. A key challenge is gener- alization to rare pathologies or different populations, noted in multiple studies, with fine-tuning on target populations suggested for improvement. However, current approaches for PD-DL training require is typically only available at specialized MRI centers that have research agreements for such data access. This is especially an issue for rural and under-resoureed areas, where commercial MRI scanners only provide access to final reconstructed image. To tackle these challenges, we propose Compressibility-insps Learning via Parallel Imaging Fidelity (CUPID) for high-quality PD-DL training using only routine clinical reconstructed images exported from an MRI scanner. CUPID evaluates output quality with compressibility- based approach while ensur- ing that the output stays consistent with the clinical parallel imaging reconstruction through well-designed perturbations. Our results show CUPID achieves similar quality to established PD-DL training that requires k-space data while outperform- ing compressed sensing (CS) and diffusion-based generative methods. We further demonstrate its effectiveness a zero-shot training setup for retrospectively and prospectively uub-sa acquisitions, attesting its minimal training burden. As an approach that radically deviates from existing strategies, CUPID presents opportunity to provide broader access fast MRI for remote and rural popula- tions in an attempt to reduce the obstacles associated with this expensive imaging modality. Code is available at htttpps: /tttps://gthubb com/ wal.calarr///UUPP111
raw k-space measurements, which
Unsupervised
Introduction
Magnetic resonance imaging (MRI) is central tool in modern medicine, offering multiple soft tissue contrasts and high diagnostic sensitivity for numerous diseases. However, MRI is among the most expensive medical imaging modalities, in part due to its long has shown an annual growth rate of 2.5%, while the number of MRI units per capita has increased by 1.8% in similar time frame (55). This mismatch has further increased the wait times for MRI exams 14 (42), particularly in rural areas and under-ressourced//emttt communities [7], shown in Fig. Thus, techniques for fast MRI scans that reduce overall scan times without compromis- ing diagnostic quality [6] are critical for improving the throughput of MRI. Computational MRI approaches, including partial Fourier imaging [56], parallel imaging [61 34 compressed sensing
times. Demand for MRI scans
(CS) 53 and more recently deep learning (DL) 38 63 have been developed for accelerating MRI.
"Coresponding Author
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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In most MRI centers, parallel imaging remains the most widely used approach for the reconstruction of routine clinical images. The acceleration rates afforded by these methods, however, are limited due to noise amplification and aliasing artifacts. DL-based methods, especially physics-driven DL (PD-DL) approaches, offer state-of-te the-are art improvements over parallel imaging 48 However, the translation of PD-DL to clinic has heen hindered by generalizability and artifact issues related to details not well repre- sented in training databases, in other words when faced with time [31 49 59 [I.. This is a problem for many typical MRI centers, whose population characteris- tics do not necessarily align with specialized MRI centers in urban settings, where training databases for PD-DL are currently curated.
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Figure I: Many regions lack direct MRI access rely local/mobile units: (a) Over half of MRI services in Min- nesota are in non-urban areas [17], and (b) these scanners often lack vendor agreements for raw data access, limiting AI fine-tuning.
samples test
In such cases, fine-tuning of the PD-DL model on the target population may be beneficial [47 25 74 19. However, a major roadblock for this strategy that all current training methods for PD-DL require access to raw MRI data. Such access requires research agreements with MR vendors, and is typically not available outside specialized/academie MRI centers. This is especially an issue for rural and under-resourced areas, where commercial MRI scanners only provide access to a final image, reconstructed via parallel imaging.
In this work, we tackle these challenges associated with typical PD-DL training, and propose Compressibility-insiiee Unsupervised Learning via Parallel Imaging Fidelity (CUPID), which trains PD-DL reconstruction from routine clinical images, e.g., in Digital Imaging and Communications in Medicine (DICOM) format. Succinetly, CUPID uses a compressibility insspieed term to evaluate the goodness of the output, while ensuring the output is consistent with parallel imaging via well-designed input perturbations. CUPID can be used both with traaaas--traiing and in subject-specific/zer shot manner, attesting to its minimal fine-tuning burden. Our key contributions include:
We introduce CUPID, a novel method that enables high-quality training of PD-DL reconstruction settings. By using only routine clinical reconstructed MR images, CUPID eliminates the need for access raw k-space measurements. To the best of our knowledge, our method is the first attempt to train PD-DL networks using only these images that are exported from the scanner.
in unsupervised and aero-shot/subject-ppeiii
CUPID is trained on DICOM images acquired at the target acceleration rate, which often have noise and aliasing artifacts due to high sub-sampling in an unsupervised manner. Note this is deviation from other methods that use reference fully-sampled DICOM images to train a likelihood score function, such as generative models.
CUPID uses a novel unsupervised loss formulation that enforces fidelity with using parallel imaging algorithms via carefully designed perturbations, in addition to evaluating the compressibility of the output image. This parallel imaging fidelity ensures the network does not converge to overly sparse solutions.
We provide a comprehensive evaluation encompassing both retrospective and prospective acquisi- tions at target acceleration rates, along with expert radiologist assessments and pathology cases from FastMRI+ [79], demonstrating that CUPID achieves reconstruction quality comparable to leading supervised and self-supervised methods that require raw k-space data, while outperforming conventional CS techniques and diffusion-basee generative methods.
2 Background and Related Work
2.1 MRI forward model and conventional methods for MRI reconstruction
MRI raw data is acquired in the frequency domain of the image referred to as k-space. For fast MRI, data is acquired in the sub-Nyquis regime by undersampling the acquisition in k-space. In this

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case, the forward acquisition model relating the image x E C to these raw MRI data (or k-space) measurements is given as:
Yn = E + n,
(1)
where yn denotes the acquired k-space data corresponding to the undersampling pattern Z with [o] = m < n. En denotes the multi-coil encoding operator that includes information from ne receiver coils, each of which are sensitive to different part of the image [37]. When the acceleration rate R = n is less than ne. this system of equations is over-determined due to the redundancies among the receiver coils. Parallel imaging uses these redundancies to solve the maximum likelihood estimation problem under i.i.d. Gaussian noise [6]]
XpI arg min Iyy Eax1 (EA En) " yn-
Numerically, this can be solved directly for certain undersampling patterns 6 or more broadly iteratively using conjugate gradient (CG) [60]. Using the equivalence of multiplication in image domain and convolutions in k-space [68], it can also be solved as an interpolation problem in k- space B4. Parallel imaging remains the most clinically used acceleration method for MRI, with some MR systems using the image-based reconstruction, while others utilizing the equivalent k-space interpolation.
In modern computational MRI, additional regularization is often incorporated into the objective function 39
arg min lyv E R(x),
where R(-) denotes regularizer. For instance, CS uses the idea that images should be compressible in an appropriate transform domain [53], and uses R(x) = T|| 1. where T is the regularization weight, W is linear sparsifying transform such as a discrete wavelet transform (DWT) and || is the l norm.
2.2 PD-DL reconstruction via algorithm unrolling
Among different PD-DL methods 3
33
48 unrolled networks [58] remain the highest performer
in reconstruction challenges 33
59 These methods unroll iterative algorithms for solving the
regularized least squares objective in Eq. (3) [32], such as proximal gradient descent [63 43 or
variable splitting with quadratic penalty (VS-QP) [2] over fixed number of steps. Unrolled networks are conventionally trained using supervised learning over a database, where the reference raw k-space measurements are first retrospectively undersampled form yn. Subsequently, the network is trained to map to the original full reference k-space or the corresponding reference image 38 minimizing:
77 by
min EE [L (yret, (f Eq; 0)))
where O are the network parameters, f(ys,, En; 0) denotes the network output for inputs yn and En. Ena is the fully-sampled encoding operator, Y is the fully-sampled reference k-space data, and L(.,) .) is a loss function.
2.3 Self-supervised and unsupervised methods
Obtaining fully-sampled reference data in MRI can be infeasible due to prolonged scan durations, organ movement in acquisitions such as real-time cardiac imaging or myocardial perfusion (62), or signal decay in acquisitions like diffusion MRI with EPI [69]. To enable training of PD-DL networks without fully sampled raw MRI data, a variety of unsupervised learning methodologies
have emerged [5) including self-supervised learning techniques 75 20 and generative modeling
approaches 45 23 22).
Self supervieed methods generate supervisory labels from the undersampled data itself 75 20 57
A pioneering method in this field, self-supervision via data undersampling (SSDU) 75 73 involves
partitioning the acquired measurement indices Ω into two disjoint subsets (S = A U θ) to train the
network in a self-supervised manner:
min E [y EA (y Ee; 0))]
(5)
3

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Even though these self- superviper based approaches demonstrate exceptional performance across various tasks, they lack the ability to train the model without access to undersampled raw data, as they cannot operate solely using images that are exported from the scanner.
Conversely, generative methods learn the prior distribution of the given dataset, which is then leveraged in conjunction with log-likelihood data term during the testing phase. Although recent methods based on diffusiin/sccre--aasee models have shown substantial promise, these methods require large amounts of high-quality images either reconstructed from raw data [45] [2] or as DICOMs (25 as well as computational resources to perform the training, both of which may not be feasible in the setups we are focused on.
3 Methodology
3.1 Why is it important to train PD-DL networks without raw k-space data?
A major limitation in the clinical adoption of deep learning (DL)-based MRI reconstruction is the issue
41 80]. Models trained on data from a specific scanner, patient population, acquisition protocol often fail when applied to different settings due to distribution shifts [1]. This lack of robustness can lead to artifacts or hallucinations which are false structures
of generalizability [3X 46 47
55
26
that resemble real anatomy, but not present in the underlying data 47
41 51].
Studies have shown that pre-trained models struggle to adapt to real-world variations, particularly in imaging protocols differ from the
centers where patient demographics, scanner configurations, original training data [41). This limitation was highlighted in the FastMRI challenges in the transfer track [59]. where networks trained on images from one vendor failed to generalize to data from another. Traditional solutions involve fine-tuning models with additional raw k-space data from the target domain 27 74, but this is infeasible in many clinical environments. While all MRI scanners inherently sample k-space data, the majority of scanners outside specialized academic or research institutions (e.g., as those in local hospitals and mobile MRI units) lack the ability to export this data due to vendor restrictions [72). As a result, most DL-based reconstruction methods, which typically rely on raw k-space during training or fine-tuning, cannot be applied in these settings.
Outside the context of PD-DL methods, diffusion models as generative priors offer an alternative in this setting. Initial promising results 45 23 66) have suggested more robustness to sampling pattern shifts, and some robustness to anatomy changes, though more recent works have argued that diffusion priors also face generalizability issues for out-of-distribution samples [3]. Thus, while promising, the robustness of the learned prior to distribution shifts, as well as the heuristic tuning of data fidelity parameters during posterior sampling, require further investigation. Furthermore, diffusion models are trained on either raw data 45 I. fully-sample magnitude (23 or complex-valie valuudd [2 10 36
DICOMs. However, they have not been trained on sub-sampled DICOMs that still contain artifacts, as explored in this work. Finally, there are other challenges for the clinical applicability and acceptance of diffusion models in MRI, including the longer inference times compared PD-DL, and more importantly the stochasticity of the output.
In light of these, training/fine-tune tuning PD-DL networks without raw k-space data is not just matter of convenience, but a necessary step toward ensuring that DL-based MRI reconstruction can generalize across diverse clinical settings.
3.2 Training without raw k-space data
In this study, we introduce novel framework train PD-DL models, utilizing only routinely available clinical images exported directly from MRI scanners. Recently, inspired by the connections between PD-DL and compressibility-ban proposed to evaluate the goodness of unsupervised PD-DL training [9]. However, this approach still requires access raw k-space data to stabilize training, making unsuitable for our goals. Here, we adapt the compressibility idea and augment it with parallel imaging fidelity to successfully reconstruct clinical images in DICOM format without needing any raw k-space data.
processing (35,, a compressibility
loss was
Compressibility aspect of the loss formulation Compressiblityyspasitt the output of the PD-DL network can be enforeed by utilizing weighted & norm 9 which has been demonstrated

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a) Compressibility
b) Paratlel Imaging Fidelity
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Update Parameters,
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Update
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W
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Figure Our setpresssibiiity-snpiiii Unsupervised Learning via Parallel Imaging Fidelity (CUPID) method trains PD-DL models in unsupervised and/or zero-shot manner without requiring any raw k-space data. The network is unrolled for units, with each unit consisting of regularizer (R) and data fidelity (DF). The proposed loss function comprises two terms: (a) reweighted l component that assesses the compressibility of the network's output; (b) fidelity term that ensures the output stays consistent with parallel imaging reconstructions via carefully designed perturbations, thereby preventing the network from producing a sparse all-zeros output.
to provide a closer approximation to the in norm compared to the standard & norm 18 Thus, this compressibility of the output image in CUPID is achieved by the loss term
1 N
N
(XP., Ea))al ((x((m))
Lcomp XpI, m) =
Σ TL-1
(6)
where denotes the DICOM input acquired using parallel imaging, W represents the wavelet transform, N the total number of wavelet coefficients and (m) signifies the signal estimate following the training during the mh reweighting step. Similar I8] we chose the initial weights from a CS reconstruction that has a large regularization and is added for numerical stability. Note, here redefined f(---) without the network parameters, and used Xpr the network input instead of ys, to simplify notation.
Parallel imaging fidelity via perturbation equivariance Relying solely Eq. (6) will result in inaccurate training as the neural network learns to produce an all-zeros image in an effort to drive the wavelet coefficients in the numerator zero, which minimizes the loss function in Eq. (6) In (9). fidelity with raw k-space data was used to avoid this training issue. In our setting without raw k-space access, introduce novel fidelity operator that stabilizes the training of the reconstruction algorithm, building on ideas from parallel imaging. Specifically, we define a secondary loss term that enforces parallel imaging fidelity formulated as:
(Xrr = Ep [|lp D 1=11l///pp]])]
where nd* = f +p. En) f(pII. Ep To motivate this loss term, we build upon the theoretical foundation of equivariant imaging (EI) [0]. In EI, an equivariance property for the composition of the forward operator and the reconstruction network is assumed with respect to transformation
group, and necessary conditions are derived for signal recovery (0
Our work adapts this framework by introducing novel transformation group tailored to parallel imaging (PI) in MRI. We note that parallel imaging reconstructions exhibit an equivariance property with respect to specific group of perturbations P = { which are designed to ensure that their R-fold aliasing do not create overlaps in the field-of-view. For p P. let Tp(x) + p be the affine perturbation from this group. Our parallel imaging fidelity then assumes equivariance of the reconstruction network to perturbations from this group as follows:
S(Tp (Xpi), En) = f(xP + p. En) = [xx, En) p = [J En)),
Our second loss term, defined in Eq. 77) promotes this equivariant behavior by penalizing deviations from this property. We also note this set of perturbations satisfy the necessary conditions in (20). In
5

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doing so, it implicitly encodes parallel imaging consistency without relying on access to raw k-space data. Our final loss function for CUPID is:
LCUPID Leomp + A Lpif;
where À is trade-off parameter between two terms.
Perturbation design specifies The perturbations used for R-fold acceleration are constructed to avoid aliasing overlaps in the field-of-view, ensuring they are resolvable via parallel imaging. This design aligns with the equivariance assumption introduced above: the network should recover an accurate estimate of x from XpI. and x + p from XpI + p. Both cases are illustrated in Fig. 2
From implementation perspective, the expectation over p is calculated over K such perturbations {p&}. The fold-over constraint for each }p&} is achieved by picking the perturbations as randomly rotated and positioned letters, numbers, card suits other shapes that have different intensity values. These choices also ensure that by the regularization process. Further information on this is given in Appendix
information, such as edges, are accurately reconstructed
shiffee--peeifficzzzroosstttt application In resource-limitee settings, it may be more practical to fine-tune the method using only a few subjects, even single subject, to significantly reduce computational costs. As Eq. 6 does not solely focus on the subtraction between two entities, it lacks an inherent mechanism drive the loss to zero through overfitting. Therefore, CUPID can be tailored to suit a scan-specific context 4 without any modification to the loss given in Eq. (9).
Evaluation
4.1 Experimental setup and implementation details
We conducted thorough evaluation of our method, assessing its performance through both qualitative and quantitative analyses, and focused on uniform/equidistant patterns which produces coherent artifacts that are more difficult to remove compared to the incoherent artifacts from random under- sampling 47).
Retrospective undersampling setup In our retrospective studies, we used fully-sampled multi-coil knee and brain MRI data from the fastMRI database, acquired with relevant institutional review board approvals [49] 78). Knee dataset included fully-sampled coronal proton consity-weighher (coronal PD) and PD with fat suppression (coronal PD-FS) data, both with matrix sizes of 320 x 320. For brain MRI, axial T2-weighted (ax T2) and axial FLAIR (ax FLAIR) datasets with matrix size of 320 x 320 are used. Both knee datasets comprise data collected from 15 receiver coils, while the brain datasets include data collected from 16 and 20 receiver coils for the ax T2 and FLAIR, respectively.
Every dataset was retrospectively undersampled using a uniform/equidisttan pattern at R = 4. 24 lines of auto-calibration signal (ACS) from center of the raw k-space data were kept. DICOM images to train our proposed model were reconstructed using parallel imaging (CG-SENSE), solving XpI = (EA E EA yn. For each dataset, models were trained using 300 slices, and testing was performed using 380 slices for knee MRI and 300 slices for brain MRI, from distinct subjects. More details about the implementation of the PD-DL models are provided in Appendix A
Prospective undersampling setup In this experiment, we replicate the practical pipeline for CUPID, where data is acquired at the desired high acceleration rate, and reconstructed to Xpt with noise and aliasing artifacts, using parallel imaging. To this end, a 3D MP2RAGE sequence [54] was acquired 7T Siemens Magnetom MRT scanner, with institutional review board approval, and matrix size= 320 x 300 x 224, isotropic resolution = 0.75mm, prospective undersampling R = 4 (in ky only). This is the desired target acceleration, which is higher than the standard clinical acquisition. Low-resolution images were acquired in the same orientation for sensitivity estimation [50]. Training and reconstruction with CUPID was done in a zero-shot subject-specific manner.
4.2 Comparison methods
We compared our method with several database training methods that have access to raw k-space data, including supervised PD-DL [38 2 48), SSDU [75), and equivariant imaging (EI) [20). All

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Puforence
SONGE Dos?
Corponsed
Superbbed PD-OL
35DU
CUPD
DESTO
Figure 3: Representative slices reconstructed at an acceleration factor of R = 4 using equidistant undersampling from coronal PD and coronal PD-FS knee MRI, as well as axial T2-weighted brain MRI. The baseline CG-SENSE, CS, El-trained PD-DL, and DDS suffer from residual artifacts highlighted by red arrows. PD-DL trained with CUPID improves upon them while delivering reconstruction quality comparable to supervised and SSDU-trained PD-DL.
PD-DL methods used the same unrolled network and components (Appendix A to ensure that only the training process differed for fair comparisons. We also compared CUPID with recent diffusion model based techniques, ScoreMRI 23 and DDS [2]] These train a time-dependent score function using denoising score matching raw data, and uses this score function during inference to sample from the conditional distribution given the measurements. Finally, also included conventional reconstruction methods, CG-SENSE, which was used to generate the original Xp1 as the clinical baseline comparison that is typically not clinically usable high acceleration rates (38] well CS (53)
large dataset of reference fully-sample DICOM images or
We note that all aforementioned methods use E yn for data fidelity during inference, since this what is needed to run gradient descent conjugate gradient on b--baed fidelity terms including Ye and E as seen in Eq. (2) or SuppMat Sec. Enyy yn can be formed without accessing yo by simply multiplying XpI with E. Eg. Note that Eg includes information about the undersampling pattern Ω, which is completely known from the acquisition parameters, and coil sensitivities, which can be estimated from separate calibration scans in DICOM format (50). We emphasize that what sets CUPID apart from other PD-DL strategies is that it is the only that train the unrolled network without using yo. Thus, without loss of generality, En is known both in training and in testing for all methods.
In the pero setup, we compared our zero-shot results with zero-shot SSDU (ZS-SSDU) as well as CS, and our baseline method, CG-SENSE all of which are compatible with zero-shot inference. We also include DDS and ScoreMRI for inference this setup. while noting that these diffusion priors have been pre-trained very large databases. This is done to highlight CUPID's performance and versatility, which is trained in a zero-shot manner on the given slice. All quantitative evaluations used structural similarity index (SSIM) and peak iggnal-t-noiiee ratio (PSNR). We further emphasize that CUPID does not use raw k-space data, and as a result, it does not benefit from the redundancies across multiple coils due to the lack of access multi-coil raw k-space data. Therefore, resources are further restricted, unlike the comparison methods.
4.3 Experiments with retrospective undersampling
Database results Representative results Fig. 3 show that baseline CG-SENSE, CS and El reconstructions exhibit residual artifacts, whereas DDS suffers from minor noise amplification. In

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Table I: Quantitative results for comparison methods on Coronal PD, Coronal PD-FS, PD-FS, Ax FLAIR, and Ax T2 datasets using equispaced undersampling pattern at R = 4. First 3 rows: Gold standard setup. Trained on the same organ, contrast and acceleration rate as the target population using fully-sampled or sub-sampled raw data. Mid 2 rows: Trained on the same organ the target population, using either fully-sampled raw data or fully-sampled artifact-free DICOM images. Last rows: No access to raw data; only sub-sampled DICOM images with artifacts. The best and second-best values are highlighted, excluding the gold standard setup.
Cor PD, Knee MRI
Cor PD-FS, Knee MRI
Ax FLAIR, Brain MRI
Ax T2,
Brain MRI
Method
PSNR1
SSIM
PSNR1
SSIM
PSNR1
SSIM
PSNR1
SSIM
Supervised
40.44
0.964
35.72
0.893
37.91
0.967
36.77
0,933
SSDU 775
39.64
0.957
35.68
0.892
37.55
0,964
36.59
0.931
EI 20
38.07
0.938
33.83
0.849
36.40
0,953
34.58
0.909
ScoreMRI 23
37.85
0.928
35.01
0.883
35.26
0.934
33.83
0.899
DDS
38.64
0.950
34.89
0.875
36.18
0.950
35.16
0.914
PI 60 34
35.51
0.909
29.48
0.735
31.97
0.906
31.02
0,833
CS 53
36.92
0.922
33.31
0.841
33.17
0.929
33.61
0.897
CUPID (ours)
38.82
0.952
35.04
0.880
36.49
0.957
35.31
0.921
contrast, CUPID successfully eliminates these artifacts from the CG-SENSE image using a well- trained PD-DL network, achieving state-of-the-ar reconstruction quality comparable to supervised PD-DL and SSDU, despite only having access to Xpi for training, and not to raw k-space data unlike these other methods. We observe that parallel imaging reconstruction is not clinically usable higher acceleration rates, but is improved using CUPID-trained PD-DL reconstruction. Quantitative results in Tab. I support visual observations, showing that CUPID consistently outperforms CG-SENSE, CS, and El across multiple datasets. It also outperforms ScoreMRI and DDS across various scenarios in the majority of cases, while achieving performance comparable supervised PD-DL and SSDU, both of which have access to raw data. Further qualitative results are provided in Appendix [
subjject-pcelfficzzrr-sooo learning results Fig. 4 shows zero-shot reconstruction results. CG- SENSE and CS suffer from noise amplification and residual artifacts, with CG-SENSE showing more severe degradation. ScoreMRI and DDS exhibit artifacts in coronal PD, and ScoreMRI introduces blurring in coronal PD-FS. This blurring leads to higher distortion metrics (e.g., PSNR/SSIM), which favor smoother outputs due to penalties on high- greu-frr details, reflecting the perception-distoriaee
DICOM Generated
Compressed
Reference
via SENSE Dv,))
SSDU
ScorcMRI
DD6
CUPID
Coronal
learning results for various algorithms coronal PD and coronal PD-FS knee MRI for retrospective R 4 equidistant undersampling, along with results from database-trained diffusion models on knee data. Baseline CG-SENSE, CS, ScoreMRI and DDS suffer from residual artifacts (red arrows) and blurring. PD-DL with CUPID loss successfully removes these artifacts, and functions in similar manner to ZS-SSDU.
Figure 4: Representative

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7.. CUPID again achieves superior artifact and noise reduction, closely matching ZS-SSDU quality despite lacking raw data or self-validation.
trade-off [16
2
Ablation studies We further conducted three ablation studies to examine key factors influencing CUPID's performance. The first examined the effect the number of perturbations (Appendix C.I the second explored the impact of the hyperparameter À across multiple values (Appendix (B. and the third evaluated CUPID's robustness to different sampling patterns and higher acceleration factors (Appendix FF)
4.4 Practical setting: Prospective undersampling
(3)
(b)
brain data is acquired at the target acceleration rate, reconstructed via parallel imaging and exported in DICOM format for zero-shot fine-tuning. Fig. (hoss reconstruc- tion results for the vendor parallel imaging recon- struction, well as CS,, DDS and CUPID. Vendor- provided R = reconstruction on the scanner ex- hibits residual artifacts in Fig. AA (shown in zoomed insets). CS effectively reduces noise but results in an overly-smooth reconstruction. DDS slightly mitigates the artifact and reduces noise, but both re- main present. Our proposed CUPID method deliy-
As discussed in Section 4.1
MP2RAGE, Brain MAI
(c)
(d)
ers the most effective artifact and noise mitigation in the DICOM image without requiring any raw k-space data, demonstrating its real-world effec- tiveness. We note that ZS-SSDU cannot be applied here due to the unavailability of raw data. We also note that the cendor-providee DICOM was gener- ated using k-space interpolation [34] instead of the
Figure 5: Prospective acceleration results for various methods that operate on parallel imaging- recenstueree DICOMs exported from the scanner. (a) Vendor-providee PI DICOM (R = 4), (b) CS, (c) DDS, and (d) CUPID.
image domain formulation in Eq. (2.. Due to their equivalence, this did not cause any issues for CU- PID, as expected. Furthermore, vendor- sendor-prvvied DICOMs may also include additional zero- pard-pg naturally, as well as additional filtering/processing More information related on these aspects is given in Appendix D and Appendix G
(65). which physics physics-based based approach handles
Reference
9000 PD
4.5
Out-of-distribution (OOD) example
We further illustrate the generalizability issues dis- cussed in Section 3.1 with a representative out-of- distribution example, intended to emulate the trans- fer from urban training datasets inference in rural setting, where scanner hardware and acquisi- tion protocols often differ. Specifically, in Fig. 6 we demonstrate how SSDU and supervised PD-DL models trained on 3T coronal PD data struggle when applied to 1.5T data with a different SNR, leading to noticeable artifacts. DDS, trained on both 3T and 1.5T data, does a better job of mitigating this issue, though some performance degradation persists. CU- PID, zero-shot trained on the given slice without the need for raw data, performs the best, effectively re- ducing artifacts and maintaining high image quality.
Coronal PO, Iose 1993
DDS
CURD
Figure 1.5T OOD example showing CU- PID's superior artifact reduction.
4.6 Qualitative radiologist readings including FastMRI+ pathology cases
To assess the clinical plausibility of CUPID's results, we consulted a musculoskeletal radiologist and neuroradiologist, whose areas of expertise align with the knee and brain datasets. Both experts

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Adial FLAIN Boaia
Cocoral PD, Krew
Figure 7: Representative pathology cases from the FastMRI+ dataset [79] showing CUPID recon- structions alongside reference images for brain and knee pathologies. Qualitative expert radiologist assessments suggest that CUPID maintains diagnostic content and visual fidelity across pathology regions of interest.
independently and blindly reviewed the reconstructed images presented in this work, as well as representative annotated pathology cases from the FastMRI+ dataset [79]. and provided an evaluation of diagnostically relevant contents and overall clinical realism.
In retrospective experiments regarding database results (Fig. 3 the musculoskeletal radiologist observed that CUPID led slightly more blurring than the supervised and self-supervised PD-DL methods, though this was not deemed diagnostically significant. Furthermore, CUPID was judged superior to DDS for noise suppression and artifact reduction by both radiologists. For the zero-shot experiments (Fig. 4. the musculoskeletal radiologist reported no noticeable blurring relative to 7S-SSDU and again found CUPID yield lower noise than DDS.
For the prospective reconstructions (Fig. 5). reconstructions (C) and (D) were favored for their lower noise levels, whereas (A) identified the noisiest. The neuroradiologist preferred (D) overall, citing clearer gray-white matter boundaries and less pixelation compared to the other variants.
Finally, in the pathology evaluation (Fig. representative FastMRI+ cases were reviewed by the same sub- specsspcialssss... For the brain dataset, the neuroradiologist compared CUPID and reference reconstructions of mass and likely cyst, noting no visible differences in the pathology regions and confirming that diagnostic information was maintained. For the knee dataset, the musculoskeletal radiologist assessed meniseus tear (complex degenerative tearing of the body of the meniscus with meniscal extrusion) and detailed depiction of the articular surface, which is critical for evaluating cartilage integrity. In both cases, CUPID reconstructions were considered diagnostically similar to the references the elinically relevant areas.
5 Conclusion
In this study, proposed Compressiblliy-inspiree Unsupervised Learning via Parallel Imaging Fidelity (CUPID), a novel training strategy for PD-DL MRI reconstruction using only clinically accessible images, without raw k-space data. CUPID leverages image compressibility and carefully designed perturbations that preserve parallel imaging consistency, enabling high-quality, physics- driven reconstructions. To our knowledge, this is the first method train PD-DL networks solely from clinical images. CUPID also alleviates the training burden of generative methods, which requires a large number of data during training to capture the prior well. Extensive retrospective and prospective evaluations demonstrate the effectiveness of CUPID across diverse MRI scans and learning settings.
The authors gratefully acknowledge Dr. Jutta Ellermann and Dr. Can Özütemiz for providing expert radiologist assessments during the rebuttal stage short notice.
Acknowledgements
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A Implementation Details for Each Method
PD-DL based approaches For each PD-DL method, VS-QU QP
2
75
29
30
76
was unrolled to
solve Eq. 33. transforming it into 2 sub nub-ppoolems:
arg min (1-1) 2/2 + R(z),
(10a)
x(0 arg min llan EnxI2 x||x - -z 1
(10b)
where Eq. (10a) the proximal operator for the regularization, implicitly solved using neural networks, while Eq. (Tbb) accounts for data fidelity and has closed form solution:
x (0) (EA Ep ja) (E + JuZ ()),
(11)
which was solved using a sunjugate-gradinn (CG) method 2 with 15 iterations. Unrolled network for each method comprised 10 unrolls, while the regularizer was implemented as a CNN-based ResNet architecture [67] that had 15 residual blocks. Each layer within these blocks had 3x3 kernels and 64 channels, totaling 592,129 trainable parameters. The unrolled network was trained in an end-to-end fashion for 100 epochs. For supervised PD-DL [88 2]. the normalized E1-Z loss function was used between the reconstructed and ground truth raw k-space data 48 28
For SSDU,
| = 0.4 was used as proposed in [75]. For El 20). we modified the loss function in PD-DL networks to:
min [C (yn, xa)] 0
E (EaTgxn, (EaTOR Eq: Eg:
(12)
DEG
where š2 f f (yn, En; 0) is the PD-DL network output. First term in Eq. enforces consistency with acquired raw data, while the second term imposes equivariance relative a group of transfor- mations, { Here, [G] is the cardinality of { and / is the equivariance weight. We followed the authors' publicly available CT reconstruction code for [20), and employed 3 rotations along with 2 flips. For CUPID, dual-tree complex wavelet transform (DTCWT), which provides an over-complete representation 644 24). was selected as the sparsifying transform (W) in Eq. (6). Furthermore, x()) in Eq. (6). i.e. the initial estimate prior to any reweighting, was calculated using CS approach mentioned in Section 3 This was implemented using Eq. (13) with 10 iterations,
with 10 CG steps for data fidelity and 0.01 ||xxri oo as the soft thresholding parameter.
Compressed sensing
We solved the regularized & minimization problem given below:
arg min I| Eax||2 + | Wx|]I,
(13)
using VS-QP [32. Similar to the unrolled network, data fidelity was solved using CG, and soft thresholding was implemented on the DTCWT coefficients.
DDS We followed the original code and pre-trained score network provided by 22 in their corresponding public repository. We used 15-150 DDIM sampling steps depending on the SNR and noise level, and tuned the number of CG iterations for the best performance.
ScoreMRI For ScoreMRI implementation, we followed the original code and pre-trained network provided by (23 in their corresponding public repository and used 2000 predictor-corrector (PC)
sampling.
Each method (including CUPID) implemented using single NVIDIA A1100-XX4-80005 GPU that has a total memory of 80 GB.
B Computational Efficiency and Runtime Analysis
As noted in Section 4.2 and Appendix A PD-DL comparison methods share the same unrolled network architecture. Consequently, they exhibit identical inference times of under one second per slice once they are trained on a database. Diffusion-bas based methods, such as ScoreMRI and DDS, require substantially longer training and sampling times due to their iterative denoising processes and
21

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Table 2: Training and inference/run-ting time of comparison methods under database and zero-shot settings using a single NVIDIA 1100-XXM-800GA GPU. N/A indicates methods without dataset- level training or zero-shot configuration.
Database setting
Zero-shot setting
Method
Train [GPU hours] +
Inference +
Runtime +
Supervised 38
335 hours
seconds
SSDU 75
3.5 hours
seconds
EI 20
3.5 hours
seconds
ScoreMRI 23
~ 168 hours
350 seconds
DDS (150 NFES) 22
~ 168 hours
~ 10 seconds
zs 2S-SSDU
75
K2s-SSDL X 15 seconds
CUPID (ours)
(KCUPiD 1)x3.5 hours
seconds
(KCUPiD + 1)xx63 seconds
large model complexity. These methods often involve hundreds to thousands of sampling steps during inference, resulting in inference times that are orders of magnitude higher than PD-DI approaches.
In the zero-shot setting, ZS-SSDU serves useful baseline that, like CUPID, adapts to individual scans without dataset-level retraining. However, ZS-SSDU relies on access to raw k-space data and employs -zs-sSDU 25 k-space masks in its public implementation. In contrast, CUPID operates entirely on reconstructed DICOM images and eliminates the need for raw data while maintaining comparable zero-shot reconstruction performance.
Although zero-shot optimization intro- duces additional computation, such run- times are generally acceptable in clinical workflows where reconstructions can be completed offline, for instance when image readings occur the following day [[5]. Furthermore, CUPID introduces a control- lable trade-off between reconstruction qual- ity and computational cost, determined by the number of perturbation patterns used during optimization (denoted as KÇUPID set
(+) 2 MED 022
(b) D OTD SAL
(+)
2010
S 070.911
de] De
(f
in Tab. 2). In our experiments, KCUPID = 6, resulting in a runtime approximately 7-8 minutes per slice, de- pending on the network depth. Both factors can be adjusted to balance reconstruction fidelity against run-time.
C Perturbation Strategies
Figure 8: Representative zero-shot fine-tuning result for CUPID with varying perturbation counts (K) coronal PD knee MRI (R = 4). (a) Fully-sampled, (b) CG-SENSE, (c-f) CUPID with K 1,3, 6, 10. Fewer perturbations (K < 6) yield artifacts due to poor expectation estimates; quality improves with K, but gains become negligible beyond K = 6.
C.1 Choice
for number of perturbation patterns
The empirical expectation that approxi- mates the one in Eq. 7 is expected to con- verge the true expectation as we introduce more perturbation patterns and randomness over the choice of Fig. 8 shows the zero-shot fine- fine-tuning results of CUPID with K E (1,3, 6, 10), while Fig. 99 and Fig. |9b iblllusstrttes the corresponding PSNR and SSIM curves throughout the training epochs, respectively. As expected, using single pattern does not capture the true mean and exhibits artifacts. As we introduce more perturbations, we reduce the artifacts and noise amplification. At certain point, increasing the number of perturbations becomes counterproductive. yielding only marginal gains while significantly increasing the computation time. Thus, we opted use distinct Px patterns throughout study it offers the optimal trade-off.
22

---

0.80
9348
55H
Km6
K-6
Epocts
Epochs
(a) PSNR curves for each K value.
(b) SSIM curves for each K value.
Figure 9: PSNR and SSIM curves confirm the visual observations with respect the number of perturbations, K. Lower K values tend to perform worse and increasing K becomes redundant after a certain point.
R
R
R
R
a)
b)
RRRR
R
PRRI
R
R
R
K
R
RIR
R
R
R R
R
R
R
R
R
R
R
R
g)
h)
Figure 10: Added perturbations may consist of: (a) precisely positioned letters that have the same intensity in within each shape, (b) randomly positioned letters or (c) circles that have different intensities, (d) randomly rotated card suits. Furthermore, when accelerated by R = 4, even without ACS data, whose corresponding zerofilled image is shown in (e), these perturbations can be resolved via parallel imaging methods such CG-SENSE: (f) 20 iterations, (g) 40 iterations, (h) 80 iterations.
C.2 Design alternatives for perturbations
As stated in Section 3 added perturbations may consist of several different structures. Fig. 10 provides some of these perturbation examples, illustration of how the perturbation looks with undersampling, and how they are recovered perfectly through conventional parallel imaging methods.
We note that there was no task-specift perturbation that we used, meaning that the perturbations selected from the same set were applied all datasets given that the created perturbations do not create fold-overs at R-fold which result in artifacts. Note the latter condition means they should be recoverable through parallel imaging reconstruction. Finally, we note that when calculating the sample mean estimate for Eq. (7). intensity of the perturbations was empirically found to be more important than their shapes/orientations. Specifically, we observed that varying it randomly within the perturbation, in Fig. 10p-d, Ieads to improved reconstruction outcomes.
23

---

Reference
ORAPPA
CUPID
Figure 11: Representative reconstructions for CUPID with XpI reconstructed using GRAPPA on coronal PD knee MRI using R 4 uniform undersampling. GRAPPA exhibits aliasing and noise artifacts at this high acceleration rate. PD-DL network trained with CUPID implementation that only has access to this GRAPPA reconstruction improves on reducing these artifacts. This highlights the compatibility of CUPID with different parallel imaging reconstructions.
D Compatibility with Various Parallel Imaging Reconstructions
Vendor reconstructions typically different parallel imaging techniques. For retrospective studies, we used CG-SENSE (or equivalently SENSE) [61] because it naturally fits with the DF units in the unrolled network, and it is commonly used in clinical settings, alongside GRAPPA (34). However, we emphasize that our method does not make assumptions about the specific reconstruction method used by the vendor; instead, it assumes that parallel imaging resolve the perturbations, which ensured by designing them a manner that prevents fold-over aliasing artifacts from overlapping.
To further validate this, we include representative CUPID reconstruction results in Fig. 11 where is generated via GRAPPA [4], demonstrating that CUPID is compatible with different types of parallel imaging reconstructions as input. We further note that the prospective study also used GRAPPA reconstruction as input, as this is the reconstruction provided by the vendor used in our institution.
E Effect of the Trade-off Parameter
We explored the effect of À parameter in CUPID by training distinet PD-DL networks using E {0,50 50, 100, 200, oo}. J. We note that using À = 0 corresponds to using only the compressibility term (Lcomp in Eq. 6 whereas using X - Do translates using solely the parallel imaging fidelity term (firr in Eq. 77). Fig. 12 shows the corresponding reconstruction results for each case. As outlined in Section only using Leomp leads overly-smooth reconstructions due network forcing the wavelet coefficients towards zero without maintaining consistency with the data. On the other hand, solely using Cpif results in DIP-like reconstructions [70), where the network overfits the data without any regularization, resulting in noise amplification. CUPID with À E (50, 100, 200} combines both loss terms attain high-fidelity reconstructions. Thus, we conclude that CUPID
Reforance
SENSE
-
A= 50
100
200
10
Using only the compressibility term (A 0) the loss leads overly-smoothed images, whereas using only the parallel imaging fidelity term (A - oc) causes noise amplification (red arrows). Using both terms with mid-range value as a trade-off provides high-quality reconstructions that are clear from noise and artifacts.
Figure 12:

---

demonstrates robust performance across a wide range of À values, provided that À is chosen within reasonable range.
F Experiments on Sampling Pattern Variations and High Acceleration Rates
We further evaluated the robustness of CUPID to variations in acceleration rate and sampling pattern using the fastMRI knee and brain datasets 49 Representative zero-shot reconstruction results for these settings are shown in Fig. 1
Specifically, we tested:
Random uniform undersampling at an accelcration rate of R = 4 (in contrast to the equidistant pattern used in the main text),
Equidistant undersampling higher acceleration rates of R 6 and R 8.
For random uniform undersampling at R = 4, the results were comparable to those obtained with equidistant sampling, exhibiting similarly clean reconstructions with effective noise suppression and minimal artifacts. At R = 6, CUPID continued to produce high-quality reconstructions, preserving image sharpness and structure with only minor residual artifacts.
At R = 8, CUPID still achieved effective noise suppression but exhibited visible residual arti- facts in some regions, indicat- ing that this acceleration fac- tor likely represents the practi- cal limit with the current coil configurations and SNRs on the fastMRI datasets. The ob- served degradations arise pri- marily from the increasing loss of quality for the parallel imag- ing reconstruction at high accel- eration, which weakens the ini- tialization, and from the general limitations of DI.-based meth- ods in highly underdetermined regimes. Previous studies have shown that supervised PD-DL methods yield visible blurring and reduced diagnostic quality at R = [59], while self- supervised approaches trained with raw k-space data also exhibit residual aliasing at this rate 75 g Since CUPID operates without any access acceleration rates is expected. Overall, these results demonstrate that CUPID generalizes effectively across sampling patterns and maintains strong reconstruction performance up moderate accelera- tion factors, with performance degradation at very high acceleration factors consistent with known challenges in highly accelerated MRI reconstruction.
DICOM (pp)
(Uniforn Unnfornandoon Random)
Conoaal PD-15, ROne MSa
36 50.07A0 370
35 000300
Contral PO, Rome MBI
R-8
25,2000 640
30,08/0 DAG
Aca T2, Bashn
R-6
Figure 13: Representative reconstructions from the fastMRI dataset for different acceleration rates and sampling patterns, illustrating robustness up R Artifact emerge at R 8, as expected.
k-space measurements, similar slightly greater degradation at extreme
G Limitations
We note some practical aspects for the translation of CUPID. While our method aims to improve equitable access to fast MRI in low-resource settings, we acknowledge hardware limitations for fine-tuning PD-DL models; however, since CUPID only requires anonymized DICOM images, data can securely transferred to off-site locations with greater computational resources. In addition, when a reference calibration scan is unavailable, as in most DICOM databases, coil sensitivities must be estimated during reconstruction. This is addressed in standard PD-DI. with raw k-space access [4 [2]. but outside the scope of this study.
25

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MR scans may also include filtering operations applied by some vendors that affect the assumption Xp = EE En) yo. This was discussed extensively in [65]. in the context of using retrospective undersampling of DICOM images to train DI. reconstruction, especially highlighting the use of zero-padding, which improves the display resolution compared to the acquisition resolution. was shown that training of models from retrospective undersampling of DICOM image databases for PD-DL training using zero-padding may lead to biases and inaccuracies. Conversely, our approach is physics-driven in nature, and the sampling pattern Ω naturally accounts for the zero-padding operation. However, our method is not immune to other types
such as implicit intensity correction [40] or deidentifiiation methods [71], in which case the filtered Xp1 would need to be treated as the parallel imaging solution corresponding to a filtered version of
H Additional Quantitative Analysis with Standart Deviation
To provide more comprehensive comparison, Tab. reports the mean and standard deviation for all quantitative metrics across four datasets. This supplements Tab. by quantifying the consistency of each method.
Table 3: Quantitative results with standard deviations for all comparison methods on Coronal PD, Coronal PD-FS, Ax FLAIR, and Ax T2 datasets using equispaced R 4 undersampling. Mean + std values are shown. Categories and highlight conventions follow Tab. in the main text.
Method
Coe PD, Knee MRI
CD FS, Kree MRI
Ax FLAIR. Brain MRI
Ax T2, Brain MRI
PSNKT
SSIM
PSNKT
SSIM
PSNRT
SSIM
PSNRT
SSIM
Supervised 21
20.44 + 3.27
0.964 +: 0,018
35.72 +: 2,89
0,893
4 0.058
37.91
+ 1.1
0.967
0.008
36,77
3.25
0,933 + 0.062
SSDU 15
39.64
3.26
0,957
0.021
35.68
1: 2.69
0,892
1: 0.060
37.55
1.76
0.961
0.009
36,59
3.11
0,31 1: 0.060
38.07
2.62
0.075
36.40
ScoreMR 22
37.85 + 3.66
0.928 d: 0.031
35.01 +: 2.46
0 +: 0.05X
35.26
1.84
0.934
0.013
33.83 =: 2.70
0.809 4: 0.065
DDS
38.64
0.026
2.50
0.875 0.064
36.18 1.95
0.950 0.012
+:
Pl M20 14
35.51 + 4.14
0.909 +: 0.047
20.48 =: 3.45
0.735 =: 0.112
31:07 +: 1.09
0.906 0.018
31.02 =: 2.49
0,831 + 0.075
CS 63
36.92
3.72
0,922 4 0.035
33.31 - 2.71
0.841 + 0.079
33.17 :: 1.79
0.929 0.013
33.61 2.61
0.897 + 0.071
CUPID (QHPP)
38,82
3.23
0,952
0.024
35.04 :: 2.45
0.880 =:: 0.059
36.49 1.72
0,957 0.009
35.31 3.09
0.921 4: 0.073
I More Results from the Retrospective Study
We provide additional qualitative reconstruction results for various methods, showcasing representa- tive reconstructions from each dataset, as illustrated in Fig. [4]
26

---

DICOM Day?
Congrecsed Senwing
CUPD
PD.
3T400
STADOSIL
X
T2,
Figure 14: Illustrative slices reconstructed at = 4 using equidistant undersampling from coronal PD and coronal PD-FS knee MRI, well as axial T2 and FLAIR brain MRI. CG- CS. El and DDS exhibit artifacts. On the other hand, CUPID surpasses them with high-fidelity reconstructions, closely matching supervised and self-supervised PD-DL. methods that require raw k-space data during training.
27


Reviews:
[{"review_id": "NKHdJ2aIyb", "reviewer": "Reviewer_YS9T", "summary": "The paper introduces CUPID (Compressibility-inspired Unsupervised Learning via Parallel-Imaging Fidelity), a training strategy that lets physics-driven deep-learning (PD-DL) MRI reconstructions be fine-tuned or even trained from scratch using only routine scanner reconstructions (DICOMs) instead of raw k-space. CUPID (i) enforces compressibility with a re-weighted ℓ1 loss and (ii) adds an equivariant “parallel-imaging fidelity” loss based on carefully crafted, non-aliasing perturbations, so the network cannot collapse to a trivial sparse solution. Because it needs only DICOMs, CUPID could facilitate fast-MRI in settings where vendors will not release raw data. One thing i really like is that this paper did prospective undersampled reconstruction study, thats really important for clinical application - though i didn't fully buy the results, also the ood experiments are informative.", "questions": "1. I'm curious on the perturbation patterns, can it be also learned?", "limitations": "the most important one is the improvements are subtle to me compared to other appraoches.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\n1. This paper is kinda dense, but contains a wide range of experiments, reading it through, it might not be the most clear one, but i can get all the core ideas, i would say its a well written paper.\n2. As I mentioned before, I love the experiments and figures the authors presented for prospective undersampled reconstruction, instead of only evaluating on fast MRI, also the OOD experiments.\n\nWeaknessness:\n1. I didn't buy the idea of this rural region, you claimed that finetuning will be needed for those scanners, but i didn't see a valid proof of why this is the case, maybe one way to do is to collect some data from a different scanner and just show this point?\n2. I appreciate the prospective study, but to be honest, i didn't see an advantages of CUPID compared to other approaches, and there is only 1 figure showing that, i would appreciate more examples.\n3. Most the experiments are done with R=4, maybe try other undersampling factors?\n\nMinor comments\n1. Fig. 2 caption could define λ and K explicitly.\n2. Typo L288 “improved using a CUPID-trained” → “an”.\n3, Listing GPU hours in Appendix A would be helpful.", "was_revised": true, "final_justification": "I appreciate the authors for the feedback, after going through the rest of the comments, i would love to change my rating to borderline accept!", "rebuttal": "**W1. The need for fine-tuning without raw data and importance of CUPID**\n\nWe thank the reviewer for raising this important point. As described in Section 4.5 and illustrated in Figure 6, **we readily simulated the out-of-distribution scenario suggested by the reviewer**, where we trained PD-DL models on 3T coronal PD data and tested on 1.5T data. This domain shift introduces changes in SNR and system characteristics, leading to visible artifacts in supervised and self-supervised PD-DL reconstructions. CUPID, by contrast, adapts to this change by training on DICOMs and produces significantly improved reconstructions.\nWe would like to highlight that CUPID assumes access to only subsampled DICOM images, without access to raw k-space, reflecting a common constraint in rural or resource-limited settings. While fine-tuning using raw data may be possible in theory, it is often infeasible in such clinical workflows due to limitations in *vendor agreements, privacy concerns, and storage resources*. We additionally want to emphasize that in addition to scanner hardware differences suggested by the reviewer and simulated in the paper, patient demographics and institution-specific imaging protocols are more likely to contribute to distribution shifts between urban training datasets and rural applications. CUPID is designed to handle such variability by enabling robust adaptation without access to raw data, aiming to be a practical and scalable solution for diverse clinical settings.\n\n**W2. Advantage of CUPID in our prospective study and further neuroradiologist assessment**\n\nWe thank the reviewer for their comment regarding the prospective study. Although only a single example could be included in the main submission due to space constraints and limited availability of prospective data, we believe it serves as a representative case. **During the rebuttal period, we conducted a blinded review with a neuroradiologist**, who evaluated the prospective reconstructions. Specifically, for Figure 5, the radiologist favored (C) and (D) due to their lower noise levels, whereas (A) was reported to have the most noise. **They preferred (D) overall, citing better visualization of the gray–white matter boundary and less pixelation** compared to (A), (B) or (C). These comments suggest that **CUPID offers visual and diagnostic advantages in prospective data**.\n\nIn addition to the prospective case, we also conducted a **broader blinded evaluation** with both a **musculoskeletal radiologist** and the **neuroradiologist**, who **independently reviewed the original submission images and several annotated pathology cases from FastMRI+** (DOI:10.1038/s41597-022-01255-z). For the brain dataset, a neuroradiologist reviewed CUPID and reference reconstructions of a mass and a likely cyst, reporting **no noticeable difference in the zoomed-in pathology regions** and confirming that diagnostic content was preserved. Similarly, for the knee dataset, a musculoskeletal radiologist reviewed pathologies marked as a meniscus tear (complex degenerative tearing of the body of the meniscus with meniscal extrusion). There was also a depiction of detail of the articular surface, which is important for assessment of articular cartilage integrity. The CUPID reconstructions were found to be **diagnostically similar** to the references in the relevant regions for these cases. While we are unable to include additional figures due to NeurIPS's rebuttal policy, we will incorporate the radiologist feedback and the results of our additional pathology-focused evaluations in the camera-ready version.\n\n**W3. Experiments with different undersampling factors**\n\nWe thank the reviewer for the insightful suggestion to evaluate CUPID under different undersampling factors. During the rebuttal period, we conducted additional experiments on fastMRI dataset using:\n\n•\t**Random uniform sampling** (instead of equidistant) **at R=4**\n\n•\t**Equidistant sampling at R=6 and R=8**\n\nOur results indicate that **CUPID generalizes well to these variations**. Specifically, performance under R=4 (random uniform) and R=6 remains consistent with the trends reported in the original submission. At R=8, we still observe effective noise suppression, though residual artifacts persist, suggesting that this may represent the method’s practical limit under the current configuration for the fastMRI datasets.\nWe believe this degradation is due to both the increased difficulty of the parallel imaging reconstruction at high acceleration factors, which leads to a weaker initialization, and the general limitations of deep learning-based reconstruction in highly underdetermined regimes. Previous studies have shown that supervised PD-DL methods produce visible blurring and diagnostically unusable images at R=8 (DOI: 10.1002/mrm.28338). Similarly, self-supervised methods also suffer from residual aliasing at this rate, even when using raw k-space data (DOI: 10.1002/mrm.28378). Thus, as a PD-DL method that does not utilize any raw k-space data, CUPID is expected to encounter similar or greater challenges under such extreme undersampling. Again, we are unable to include any figures or visual examples due to NeurIPS's rebuttal policy. However, we will include these extended experiments and observations in the camera-ready version.\n\n**Q1. Learnable perturbation patterns**\n\nWe thank the reviewer for this interesting suggestion. In the current formulation, perturbation patterns are hand-crafted to ensure PI resolvability. However, we also believe that extending CUPID to learn perturbation patterns is a promising direction. This could potentially allow for task-adaptive or anatomy-aware regularization, and we plan to explore this in future work.\n\n**Minor Comments**\n\nWe thank the reviewer for these suggestions. We will clarify or correct where appropriate and include GPU training times for the camera-ready version."}, {"review_id": "e5FqLoLK02", "reviewer": "Reviewer_1rYs", "summary": "This paper proposes an unsupervised MRI reconstruction technique that leverages only undersampled, clinically reconstructed images for training that are readily available in routine scans. Thus, training is possible without modifying the scanning protocols, typically only possible in hospitals involved in academic research. Experiments on undersampled knee and brain MRI images show promising results compared to other untrained methods.", "questions": "- How does CUPID compare to baselines under different scan patterns and acceleration ratios? Moreover, comparison of reconstruction times/compute effort required would be useful.\n- Are the reconstructions clinically valuable besides the promising distortion metrics?", "limitations": "Limitations are discussed in the Appendix.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 4, "originality": 3, "strengths_and_weaknesses": "Strengths:\n- This work has potential for practical impact. Obtaining raw, fully-sampled kspace data from scanners at large scale is challenging and requires close collaboration with hospitals. Thus, reconstruction techniques that can leverage more easily accessible data from the scanners are highly valuable.\n- The proposed methodology is sensible and the experiments demonstrate clear improvements over untrained baselines in the investigated settings.\n- The paper is mostly well-written and easy to follow. \n\nWeaknesses:\n- The experiments are limited to a single undersampling ratio and scanning pattern. It would be interesting to see how CUPID performs in more diverse scenarios, such as random sampling instead of equidistant (or other popular scanning patterns), and higher/lower acceleration ratios (say R=2 and 8). \n- It would be crucial to have the reconstructions evaluated by radiologists and compared to traditional reconstructions in clinical practice. Promising evaluation from experts would provide strong support for this work.\n- Minor: typo on line 144, font size in Fig. 2 is too small.", "was_revised": true, "final_justification": "Authors addressed my issues with respect to additional experiments on scan patterns and accelerations, as well as radiologist evaluation, thus I increased my score to Accept.", "rebuttal": "**W1 & Q1. Experiments with different acceleration rates and sampling (scan) patterns**\n\nWe thank the reviewer for the insightful suggestion to evaluate CUPID under a broader range of sampling patterns and acceleration factors. During the rebuttal period, we conducted additional experiments on fastMRI dataset using:\n\n•\t**Random uniform sampling** (instead of equidistant) **at R=4**\n\n•\t**Equidistant sampling at R=6 and R=8**\n\nOur results indicate that **CUPID generalizes well to these variations**. Specifically, performance under R=4 (random uniform) and R=6 remains consistent with the trends reported in the original submission. At R=8, we still observe effective noise suppression, though residual artifacts persist, suggesting that this may represent the method’s practical limit under the current configuration for the fastMRI datasets.\n\nWe believe this degradation is due to both the increased difficulty of the parallel imaging reconstruction at high acceleration factors, which leads to a weaker initialization, and the general limitations of deep learning-based reconstruction in highly underdetermined regimes. Previous studies have shown that supervised PD-DL methods produce visible blurring and diagnostically unusable images at R=8 (DOI: 10.1002/mrm.28338). Similarly, self-supervised methods also suffer from residual aliasing at this rate, even when using raw k-space data (DOI: 10.1002/mrm.28378). Thus, as a PD-DL method that does not utilize any raw k-space data, CUPID is expected to encounter similar or greater challenges under such extreme undersampling. Due to NeurIPS's rebuttal policy restricting the inclusion of figures or PDFs, we are unable to present visual examples here. However, we will include these extended experiments and observations in the camera-ready version.\n\n**Q1. Comparison of reconstruction times**\n\nWe thank the reviewer for raising this important point. As noted in Section 4.2, all PD-DL methods use the same unrolled architecture and components to ensure a fair comparison. As a result, once trained, their reconstruction times are identical, each taking less than 1 second per slice (including data reading and saving). Among diffusion-based methods, DDS requires approximately 11.6 seconds for 150 sampling steps, while ScoreMRI is significantly slower, taking approximately 50–100× longer. Additional architectural details are provided in Appendix A, and we will include GPU training times and memory consumption comparisons in the camera-ready version.\n\n**W2 & Q2. Radiologist evaluations and further clinical pathology validation**\n\nWe thank the reviewer for this valuable comment. While we did not have sufficient time during the rebuttal period to conduct a full reader study, we consulted a **musculoskeletal radiologist** and a **neuroradiologist**, whose areas of expertise align with the **knee** and **brain** datasets used in our work. They **independently and blindly reviewed the images included in the original submission, as well as several annotated pathology cases from FastMRI+** (DOI:10.1038/s41597-022-01255-z).\n\nImportantly, the figures they evaluated included **reconstructions from traditional clinical methods** such as **parallel imaging and compressed sensing**, in addition to DL-based methods. Their expert feedback therefore reflects a direct qualitative comparison against clinically relevant reconstructions, as suggested by the reviewer, and supports the clinical plausibility of CUPID’s outputs:\n\n•\tFor Figure 3, the radiologists noted that while CUPID exhibited slightly more blurring compared to supervised and self-supervised PD-DL methods, this was not deemed diagnostically significant. Additionally, CUPID was rated superior to DDS in terms of noise suppression and artifact reduction.\n\n•\tFor Figure 4, CUPID did not exhibit noticeable blurring compared to ZS-SSDU and was again found to produce less noise than DDS.\n\n•\tIn addition, the neuroradiologist conducted a blinded review of the prospective study images given in Figure 5. Both (C) and (D) were favored due to their lower noise levels, whereas (A) was reported to have the most noise. **They preferred (D) overall, citing better visualization of the gray–white matter boundary and less pixelation** compared to (A), (B) or (C).\n\n•\tWe also shared representative pathology cases from the FastMRI+ dataset with subspecialty radiologists. For the brain dataset, a neuroradiologist reviewed CUPID and reference reconstructions of a mass and a likely cyst, reporting **no noticeable difference in the zoomed-in pathology regions** and confirming that diagnostic content was preserved. Similarly, for the knee dataset, a musculoskeletal radiologist reviewed pathologies marked as a meniscus tear (complex degenerative tearing of the body of the meniscus with meniscal extrusion). There was also a depiction of detail of the articular surface, which is important for assessment of articular cartilage integrity. The CUPID reconstructions were found to be **diagnostically similar** to the references in the relevant regions for these cases. Again, we are unable to include any figures or visual examples due to NeurIPS's rebuttal policy. However, we will incorporate the radiologist feedback and the results of our additional pathology-focused evaluations in the camera-ready version.\n\n**Minor Comments**\n\nWe thank the reviewer for their careful reading and for identifying typographical errors. These will be corrected in the camera-ready version."}, {"review_id": "pgR7NFAOxm", "reviewer": "Reviewer_Kki4", "summary": "This paper introduces CUPID (Compressibility-inspired Unsupervised Learning via Parallel Imaging Fidelity), a novel method for training physics-driven deep learning (PD-DL) MRI reconstruction networks without raw k-space data. \nCUPID leverages DICOM format images to enable unsupervised or zero-shot training. This approach is specifically designed to address the equity gap in access to state-of-the-art fast MRI, especially in rural and underserved areas where access to raw MRI data is typically unavailable due to vendor restrictions. \nThe method combines a compressibility-based loss term with a novel parallel imaging fidelity loss, aiming to ensure both output quality and physical consistency. Comprehensive experiments demonstrate that CUPID matches the performance of supervised and self-supervised methods requiring raw data and outperforms compressed sensing and generative diffusion methods, both retrospectively and prospectively. The paper argues that CUPID provides an avenue for democratizing advanced MRI acceleration technologies.", "questions": "1. In several qualitative figures, CUPID’s reconstructions appear noticeably smoother than the original images and competing methods (e.g., Figs. 3–5). Is this an inherent effect of the compressibility loss (possibly over-regularizing high-frequency details), or a consequence of DICOM-specific preprocessing? Have the authors quantitatively evaluated the potential loss of diagnostic high-frequency features (such as small lesions or vessel boundaries) and discussed the implications for clinical utility? Greater discussion and, if possible, radiologist assessment or frequency-domain analysis would strengthen the work.\n2. Question about loss normalization and the trade-off parameter \\lambda: \nSince the compressibility loss and parallel imaging fidelity loss do not appear to be normalized, the choice of \\lambda may be sensitive to dataset or architecture changes. Did you consider normalizing or automatically balancing these loss terms? Would such normalization make CUPID more robust and easier to use across different settings?", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n- This paper introduces a fundamentally new and practical solution to the lack of raw k-space data for fast MRI training/fine-tuning.\n- The authors provide thorough experiments, which demonstrate strong performance, on par with supervised/self-supervised methods requiring raw data, across several datasets and scenarios.\n- The approach combines a compressibility-inspired loss and a parallel imaging fidelity term based on perturbation equivariance, addressing a key failure mode of previous unsupervised training.\n- CUPID supports subject-specific (zero-shot) fine-tuning and is compatible with DICOM, making it truly practical.\n- The paper is well-written and organized.\n\nWeaknesses:\n- The paper does not appear to report the training cost or computational efficiency of CUPID compared to prior supervised or self-supervised PD-DL methods. As practical deployment in resource-limited settings is a key motivation, it would be helpful to provide quantitative details on training time, GPU/memory requirements, and any trade-offs with zero-shot adaptation. This information is important for evaluating real-world feasibility.\n- Figure 2 is a central illustration of the CUPID framework, but the figure and accompanying caption are difficult to read due to small font size and insufficient explanation of each component.", "was_revised": true, "final_justification": "no change", "rebuttal": "**W1. Training Cost and Computational Efficiency**\n\nWe thank the reviewer for raising this important point. As noted in Section 4.2, all PD-DL methods were implemented using the same unrolled architecture and components to ensure a fair comparison. However, CUPID differs from supervised and SSDU methods in that it requires K+1 forward passes per update step, where K is the number of perturbation patterns. As a result, CUPID’s training time and memory usage scale proportionally with K+1. For instance, while supervised and SSDU models took approximately 3.5 hours to train, CUPID required around 10–11 hours when trained with K=2, using the same hardware setup.  \nOnce trained, all PD-DL models, including CUPID, exhibit identical inference times, requiring less than 1 second per slice. In the zero-shot setting, there exists a trade-off between reconstruction quality and fine-tuning cost, controlled by the number of perturbation masks used during optimization. CUPID takes approximately 3–15 minutes per slice in this mode, depending on the number of perturbation patterns and the depth of the unrolled network. Both factors can be adjusted to balance reconstruction quality and computational cost. We will include detailed GPU training times and memory consumption comparisons in the camera-ready version. \n\nWe further acknowledge that prolonged optimization or training may pose a challenge in resource-constrained settings that lack access to high-end GPUs. However, CUPID is designed to work directly with anonymized DICOM images, without requiring raw k-space data. This enables data to be securely transferred to off-site cloud environments or central facilities with greater computational resources for model training or zero-shot inference, as discussed in Appendix E. We believe this hybrid deployment model enhances the practical feasibility of CUPID in real-world low-resource environments.\n\n**W2. Clarity and Readability of Figure 2**\n\nWe thank the reviewer for pointing this out. We will revise Figure 2 in the camera-ready version to improve readability by increasing font size and enhancing the caption with clearer explanations of each component\n\n**Q1. CUPID reconstruction quality, radiologist evaluations and further clinical pathology validation**\n\nWe thank the reviewer for the insightful questions. While we did not have sufficient time during the rebuttal period to conduct a full reader study, we consulted a **musculoskeletal radiologist** and a **neuroradiologist**, whose areas of expertise align with the **knee** and **brain** datasets used in our work. They **independently and blindly reviewed the images included in the original submission, as well as several annotated pathology cases from the FastMRI+** (DOI:10.1038/s41597-022-01255-z). Their expert feedback reinforces the clinical plausibility of our reconstructions. We summarize their impressions below:\n\n•\tFor Figure 3, the radiologists indeed noted that CUPID exhibited slightly more blurring compared to supervised and self-supervised PD-DL methods. While the compressibility loss may introduce mild smoothing, this was not deemed diagnostically significant by the radiologists. Additionally, CUPID was rated superior to DDS in terms of noise suppression and artifact reduction.\n\n•\tFor Figure 4, CUPID did not exhibit noticeable blurring compared to ZS-SSDU and was again found to produce less noise than DDS.\n\n•\tIn addition, the neuroradiologist conducted a blinded review of the prospective study images given in Figure 5. Both (C) and (D) were favored due to their lower noise levels, whereas (A) was reported to have the most noise. **They preferred (D) overall, citing better visualization of the gray–white matter boundary and less pixelation** compared to (A), (B) or (C).\n\n•\tWe also shared representative pathology cases from the FastMRI+ dataset with subspecialty radiologists. For the brain dataset, a neuroradiologist reviewed CUPID and reference reconstructions of a mass and a likely cyst, reporting **no noticeable difference in the zoomed-in pathology regions** and confirming that diagnostic content was preserved. Similarly, for the knee dataset, a musculoskeletal radiologist reviewed pathologies marked as a meniscus tear (complex degenerative tearing of the body of the meniscus with meniscal extrusion). There was also a depiction of detail of the articular surface, which is important for assessment of articular cartilage integrity. The CUPID reconstructions were found to be **diagnostically similar** to the references in the relevant regions for these cases.\n\nWhile we did not conduct frequency-domain analysis within the rebuttal period, our radiologist assessments provide strong evidence that **CUPID preserves clinically relevant high-frequency details**. While we agree that additional analysis in this direction is valuable, we are unable to include any figures or visual examples due to NeurIPS's rebuttal policy. However, we will incorporate the radiologist feedback and the results of our additional pathology-focused evaluations in the camera-ready version.\n\n**Q2. Loss normalization and the trade-off parameter $\\lambda$**\n\nWe thank the reviewer for raising this important point. While the loss terms may not appear explicitly normalized at first glance, both components of the objective are in fact **scale-invariant by design**, meaning that scaling $x_{PI}$ by a constant factor does not affect the loss, assuming the corresponding perturbations scale proportionally. Specifically:\n\n•\tCompressibility loss is normalized by 1/N and computes the average ratio of wavelet magnitudes to those from a stabilizing reference $x^{(m)}$, which is initialized via a strongly regularized CS reconstruction and updated throughout reweighting.\n\n•\tThe parallel imaging fidelity loss computes a relative $\\ell_2$ error over perturbations, normalized by the original perturbation $\\ell_2$  norm.\n\nAs a result, both losses are naturally balanced in scale and have shown consistent behavior across multiple anatomies and sampling patterns. In our experiments, the same $\\lambda$ was effective for both knee and brain datasets. While automatic weighting is an interesting direction, we found no significant sensitivity requiring such mechanisms in our current settings. We further demonstrated CUPID’s robustness to a wide range of $\\lambda$ values in our **ablation study in Appendix B (Fig. 7)**. We will clarify these points in the camera-ready version."}, {"review_id": "S1OQjDXAO4", "reviewer": "Reviewer_ex9D", "summary": "This paper presents CUPID, a novel framework to train accelerated MRI reconstruction models using only clinically available reconstructed images, which circumvents the common need for raw k-space data access. The method's core innovation is an unsupervised loss function that pairs a compressibility term with a parallel imaging fidelity term, stabilized by specially designed input perturbations. By achieving results comparable to raw-data-dependent methods, CUPID aims to bridge the equity gap and enable advanced fast MRI in underserved clinical settings.", "questions": "1.Could you provide more theoretical intuition on the design of the perturbations? What are the essential properties required for them to effectively regularize the network beyond simply being resolvable by parallel imaging?\n\n2.How does CUPID's performance degrade at acceleration rates higher than 4x, where the initial parallel imaging reconstruction serving as input would be substantially poorer?\n\n3.How would the framework perform in a common clinical scenario where separate coil calibration scans are unavailable and sensitivities must be estimated directly from the aliased images?\n\n4.For the practical zero-shot application, what is the approximate training/inference time per slice?", "limitations": "The authors provide a dedicated limitations section in the appendix that discusses practical issues like hardware constraints, the challenge of coil sensitivity estimation, and the impact of unknown vendor filtering. For improvement, the authors could further analyze the method's performance limits when the initial parallel imaging reconstruction is severely degraded and discuss the data security implications of off-site processing, which is suggested as a workaround for local hardware limitations.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 4, "originality": 4, "strengths_and_weaknesses": "Strengths: The work addresses a critical, real-world barrier to the adoption of AI in medicine—the lack of raw data access in many clinical environments. The focus on improving equity makes the contribution highly significant. The proposed parallel imaging fidelity loss, which uses perturbation equivariance to enforce data consistency without the data itself, is a clever and highly original contribution to unsupervised, physics-informed learning. The method is rigorously evaluated against a wide range of state-of-the-art techniques across multiple datasets and imaging contrasts. The inclusion of both retrospective and prospective experiments, as well as a specific out-of-distribution test, provides strong support for the claims.\n\nWeaknesses:\n1. Insufficient Intuition on Perturbation Design: While effective, the paper lacks a deep theoretical explanation for the perturbation design, relying more on empirical justification. A more formal analysis would strengthen the work. \n\n2.Performance Limits Unexplored: The method's reliance on an initial, artifact-laden parallel imaging reconstruction is a key dependency. The paper does not investigate how performance degrades as the quality of this initial input worsens, for example, at very high acceleration rates. \n3. Lack of Clinical Pathology Validation: The evaluation focuses on structural metrics (PSNR/SSIM) in largely healthy subjects. For clinical translation, an analysis showing the preservation of subtle pathological details and avoiding diagnostic omissions or \"hallucinations\" would be necessary.", "was_revised": true, "final_justification": "I appreciate the clarifications and additional details provided by the authors and maintain my original score.", "rebuttal": "**W1 & Q1. Theoretical Intuition Behind Perturbation Design**\n\nThe perturbations used in the CUPID framework are drawn from a specific class designed to ensure that their R-fold aliasing does not create overlaps within the field-of-view (FoV), making them resolvable by parallel imaging. This condition is essential for CUPID to produce meaningful results. When constructing perturbations in accordance with Equation (8), one must ensure that the aliasing pattern remains non-overlapping in the FoV for the given acceleration rate. Fortunately, this design constraint can be readily satisfied, as the undersampling pattern and acceleration factor are fully specified by the acquisition parameters.\n\nWhile the PI-resolvability condition is necessary for CUPID to function properly, further improvements in reconstruction quality can be achieved through fine-grained adjustments to the perturbation design. In particular, when computing the sample mean estimate in Equation (7), we found that the intensity and phase values of the perturbations had a greater impact than their spatial shape or orientation. Varying the intensity or phase either within a single perturbation or across multiple perturbations, as shown in Figure 10(b–d), led to notable gains in reconstruction quality. We believe this variation encourages the network to explore a more diverse response space, which in turn improves robustness and reduces the risk of overfitting to specific structures.\n\nAdditionally, we observed that sharper perturbation patterns with more high-frequency structures tended to promote sharper reconstructions. This may be attributed to the fact that sharper perturbations more strongly probe high-frequency components of the image, thereby acting as an implicit regularizer that discourages overly smooth outputs and helps preserve fine structural details.\n\n**W2 & Q2. Experiments with higher acceleration rates**\n\nWe thank the reviewer for highlighting this important aspect. During the rebuttal period, we conducted additional experiments on fastMRI dataset using:\n\n•\t**Random uniform sampling** (instead of equidistant) **at R=4**\n\n•\t**Equidistant sampling at R=6 and R=8**\n\nOur results indicate that **CUPID generalizes well to these variations**. Specifically, performance under R=4 (random uniform) and R=6 remains consistent with the trends reported in the original submission. At R=8, we still observe effective noise suppression, though residual artifacts persist, suggesting that this may represent the method’s practical limit under the current configuration for the fastMRI datasets.\nWe believe this degradation is due to both the increased difficulty of the parallel imaging reconstruction at high acceleration factors, which leads to a weaker initialization, and the general limitations of deep learning-based reconstruction in highly underdetermined regimes. Previous studies have shown that supervised PD-DL methods produce visible blurring and diagnostically unusable images at R=8 (DOI: 10.1002/mrm.28338). Similarly, self-supervised methods also suffer from residual aliasing at this rate, even when using raw k-space data (DOI: 10.1002/mrm.28378). Thus, as a PD-DL method that does not utilize any raw k-space data, CUPID is expected to encounter similar or greater challenges under such extreme undersampling.\nWe are unable to include any figures or visual examples due to NeurIPS's rebuttal policy. However, we will include these extended experiments and observations in the camera-ready version.\n\n**W3. Radiologist evaluations and further clinical pathology validation**\n\nWe thank the reviewer for this valuable suggestion. While we did not have sufficient time during the rebuttal period to conduct a full reader study, we consulted a **musculoskeletal radiologist** and a **neuroradiologist**, whose areas of expertise align with the **knee** and **brain** datasets used in our work. They **independently and blindly reviewed the images included in the original submission, as well as several annotated pathology cases from FastMRI+** (DOI:10.1038/s41597-022-01255-z). Their expert feedback reinforces the clinical plausibility of our reconstructions. We summarize their impressions below:\n\n•\tFor Figure 3, the radiologists noted that while CUPID exhibited slightly more blurring compared to supervised and self-supervised PD-DL methods, this was not deemed diagnostically significant. Additionally, CUPID was rated superior to DDS in terms of noise suppression and artifact reduction.\n\n•\tFor Figure 4, CUPID did not exhibit noticeable blurring compared to ZS-SSDU and was again found to produce less noise than DDS.\n\n•\tIn addition, the neuroradiologist conducted a blinded review of the prospective study images given in Figure 5. Both (C) and (D) were favored due to their lower noise levels, whereas (A) was reported to have the most noise. **They preferred (D) overall, citing better visualization of the gray–white matter boundary and less pixelation** compared to (A), (B) or (C).\n\n•\tWe also shared representative pathology cases from the FastMRI+ dataset with subspecialty radiologists. For the brain dataset, a neuroradiologist reviewed CUPID and reference reconstructions of a mass and a likely cyst, reporting **no noticeable difference in the zoomed-in pathology regions** and confirming that diagnostic content was preserved. Similarly, for the knee dataset, a musculoskeletal radiologist reviewed pathologies marked as a meniscus tear (complex degenerative tearing of the body of the meniscus with meniscal extrusion). There was also a depiction of detail of the articular surface, which is important for assessment of articular cartilage integrity. The CUPID reconstructions were found to be **diagnostically similar** to the references in the relevant regions for these cases.\n\nAgain, we are unable to include any figures or visual examples due to NeurIPS's rebuttal policy. However, we will incorporate the radiologist feedback and the results of our additional pathology-focused evaluations in the camera-ready version.\n\n**Q3. Handling Cases Without Separate Calibration Scans**\n\nWe thank the reviewer for this excellent and forward-looking question. We briefly discussed similar concerns in our Limitations section (Appendix E), where we stated that CUPID is designed to operate on settings where this calibration scan is available. That said, joint estimation of sensitivities and image content from aliased multi-coil data is an important and more complex extension, actively studied in recent works with raw data (e.g.,  DOI: 10.1007/978-3-030-87231-1_34). While this is outside the scope of CUPID’s current formulation, we see this as a promising and practical future direction. One potential avenue we are exploring involves initializing sensitivity estimation using known coil configurations, without relying on explicit calibration scans.\n\n**Q4. Training/Inference times per slice for zero-shot application**\n\nCUPID takes approximately 3–15 minutes per slice to produce high-quality reconstructions in the zero-shot learning setup. We emphasize that this runtime is flexible and primarily depends on the number of perturbation patterns used during optimization, as well as the depth of the unrolled network. Both factors can be adjusted to balance reconstruction quality and computational cost."}]

Author rebuttal:

Meta-review: This paper presents a novel framework, called CUPID, to train accelerated MRI reconstruction models using only clinically available reconstructed images. This circumvents the need for access to the raw k-space data, which is not widely available due to licensing and regulatory burden imposed by the device manufacturers and the government. The method's core innovation is an unsupervised loss function that pairs a compressibility term with a parallel imaging fidelity term, stabilized by specially designed input perturbations. Experiments show that CUPID achieves similar reconstruction quality as that obtained by state-of-the-art physics-derived deep learning-based methods that reconstruct from the raw k-space data. Backed by these results, CUPID aims to bridge the equity gap and enable fast MRI in underserved clinical settings, where there is no access to k-space data. 

As part of the initial review, multiple concerns were raised by the reviewers, most of which were addressed by the authors as part of their rebuttal. Some of the concerns raised were: 
- Robustness of the technique against multiple sampling factors and sampling patterns
- Clinical validity of the reconstructed images
- Lack of discussion around the training cost and computational efficiency of the method, especially since this method is motivated by its utility in under-resourced environments

All these concerns were addressed by the authors during the rebuttal, prompting some of the reviewers to upgrade their scores. 

Keeping in mind the rebuttal posed by the authors and the subsequent changes promised in the final manuscript, this is a well-motivated, technically solid work backed up by extensive experiments and ablation studies on open-source datasets. Furthermore, it has the potential for a widespread real-world clinical impact by enabling expedited MR image reconstruction in areas (such as rural America) without access to raw k-space data for custom algorithm development. Other strengths of the paper are: 
- A clearly written and well-motivated manuscript
- Introduces a fundamentally new and sensible approach to a real clinical problem 
- Extensive experimental validation, along with a small-scale reader study to validate the efficacy of the proposed approach.
- Potential for a widespread practical impact
Decision: Accept (spotlight)