SuperF: Neural Implicit Fields for Multi-Image Super-Resolution
Authors: Sander Riisøen Jyhne
Christian Igel
Morten Goodwin
Per-Arne Andersen
Serge Belongie
Nico Lang
Venue: ICLR 2026 Poster (2026)
Keywords: implicit neural representation
neural fields
super-resolution
test-time optimization
learning-free
multi-image super-resolution
Primary area: applications to computer vision, audio, language, and other modalities
TL;DR: We propose a learning-free multi-image super-resolution approach leveraging the continuous nature of implicit neural representations

Abstract: High-resolution imagery is often hindered by limitations in sensor technology, atmospheric conditions, and costs. Such challenges occur in satellite remote sensing, but also with handheld cameras, such as our smartphones. Hence, super-resolution aims to enhance the image resolution algorithmically. Since single-image super-resolution requires to solve an inverse problem, such methods must exploit strong priors, e.g. learned from high-resolution training data, or be constrained by auxiliary data, e.g. by a high-resolution guide from another modality. While qualitatively pleasing, such approaches often lead to "hallucinated" structures that do not match reality. In contrast, multi-image super-resolution (MISR) aims to improve the (optical) resolution by constraining the super-resolution process with multiple views taken with sub-pixel shifts. Here, we propose SuperF, a test-time optimization approach for MISR that leverages coordinate-based neural networks, also called neural fields. Their ability to represent continuous signals with an implicit neural representation (INR) makes them an ideal fit for the MISR task. The key characteristic of our approach is to share an INR for multiple shifted low-resolution frames and to jointly optimize the frame alignment with the INR. Our approach advances related INR baselines, adopted from burst fusion for layer separation, by directly parameterizing the sub-pixel alignment as optimizable affine transformation parameters and by optimizing via a super-sampled coordinate grid that corresponds to the output resolution. Our experiments yield compelling results on simulated bursts of satellite imagery and ground-level images from handheld cameras, with upsampling factors of up to 8. A key advantage of SuperF is that this approach does not rely on any high-resolution training data.

SUPERF: NEURAL IMPLICIT FIELDS FOR MULTI-IMAGE SUPER-RESOLUTION
Sander Riissen Jyhne University of Agder
Christian Igel
Morten Goodwin University of Agder
University of Copenhagen
Per-Arne Andersen University of Agder
Serge Belongie
Nico Lang*
University of Copenhagen
University of Copenhagen
ABSTRACT
High-resolution imagery often hindered by limitations in sensor technology. atmospheric conditions, and costs. Such challenges occur in satellite remote sensing, but also with handheld cameras like our smartphones. Hence, super- resolution aims enhance the image resolution algorithmically. Since single- image super- reper-resolution requires solving an inverse problem, these methods must exploit strong priors, c.g. learned from high-resolution training data, or be con- strained by auxiliary data, e.g. by a high-resolution guide from another modality. While qualitatively pleasing, such approaches often lead to "hallucinated" struc- tures that do not match reality. In contrast, multi-image super-resolution (MISR) aims to improve the (optical) resolution by constraining the super-resolution pro- cess with multiple views taken with sub-pixel shifts. Here, we propose SuperF, a test-time optimization approach for MISR that leverages coordinate- based neu- ral networks, also called neural fields. Their ability to represent continuous sig- nals with an implicit neural representation (INR) makes them an ideal fit for the MISR task. The key characteristic of our approach is to share INR for multiple shifted low-resolution frames and to jointly optimize the frame alignment with the INR. Our approach advances related INR baselines, adopted from burst fusion for layer separation, by directly parameterizing the sub-pixel alignment as opti- mizable affine transformation parameters and by optimizing via auper-sampled coordinate grid that corresponds to the output resolution. Our experiments yield compelling results on simulated bursts of satellite imagery and ground-level im- ages from handheld cameras, with upsampling factors of up to 8. A key advantage SuperF is that this approach does not rely on any high-resolution training data]
INTRODUCTION
The spatial resolution of imaging is often limited by sensor capabilities, atmospheric interference, and acquisition costs, affecting various domains including satellite remote sensing, smartphone pho- tography, and medical imaging. Super-resolution (SR) aims overcome such physical constraints algorithmically. Single-image super-resolution (SISR) methods tackle this inverse problem by re- lying strong priors. typically learned from extensive high-resolution (HR) datasets (Ledig al. 2017 Zhang et al. 2023). or through auxiliary guidance from complementary modalities (De Lutio al. 2019 2022 Metzger al., 2023 Mei et al. 2025). Although SISR methods can produce visually appealing results, their reliance on learned priors often leads to hallucinated structures that diverge from the true underlying scene (Cohen et al. 2024). This may be tolerable for smartphone applications, but not for applications in medicine and science.
To mitigate some of these issues, multi-image super-resolution (MISR) has emerged special case of super-resolution by incorporating additional information from multiple low-resolution (LR)
images captured with slight sub-pixel shifts (Tsai & Huang 1984 Irani & Peleg 1991 Elad &
"Corresponding authors: sander. jyhne @ kartverket.nng nila@ ku.dk
"The code, dataset, and demo available on the project page: fighne-gihuuh.oosupprr

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Imput:
Coordinate
INR:
Output:
Targete:
cooddinates
transform
impliet seural
LIR RGB uneestoincy
Posleed mutch LR frames
milhippe shafted LR
HR
reprosentation
fooe base frome
aliggt
Positional eaevodaluuueiin encodiaut
Decoder
allign
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allign
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Figure 1: Illustration of the proposed method. SuperF' achieves multi-image super-resolution by sharing an implicit neural representation (INR) across multiple low-resolution (LR) frames with sub- pixel shifts. The LR frames are aligned by jointly optimizing an affine coordinate transformation for each LR frame, together with the parameters of coordinate- based multi-layer perceptron (MLP) that decodes the input coordinates to RGB values. Hence, leveraging the continuous characteristics of INRs for both the sub-pixel alignment in the pixel coordinate space and for representing underlying high-resolution (HR) signal. For robustness, the proposed INR can optionally represent additional frame-specific uncertainty maps ignore noisy pixels (e.g. clouds) in the optimization.
Feuer 1997). As sub-pixel shifts vary across the repeated LR frames, the discretization introduces different aliasing artifacts each frame. While these artifacts seem be noise in the LR data, they can be leveraged as complementary information to compute the shared underlying high-resolution image (Wronski et al. 2019).
While MISR can be approached with supervised learning- based methods (Bhat et al. 202 b) when large training datasets with paired LR and HR data are available, MISR can also be achieved by test-time optimization (TTO) approaches that do not require offline training (Wronski et al. 2019 Lafenetre al. 2023). The latter are particularly interesting, since HR data acquisition is expensive and the creation of large training datasets by pairing of LR images and HR data is non-trivial (Bhat) (ct al. 2021a). Typically, MISR associated with bursts of images captured in rapid succession. Repeated observations in satellite remote sensing also provide multi-frane scenario with longer time intervals
In this work, introduce SuperF, a test-time optimization approach for MISR leveraging the tinuous field of implicit neural representations (INR). SuperF shares an INR across multiple shifted LR frames, while jointly estimating the frame-specific alignment. Iteratively refining both the align- ment and the shared neural representation effectively reconstructs the underlying high-resolution image continuous field (see Fig. for illustration of the proposed method).
INRs are boosdinate-based neural networks, also called neural fielde typically parameterized by multi-layer perceptrons (MLPs) that map continuous input coordinates (e.g. 2D image locations) directly to signals like RGB pixel intensities. Optimizing the parameters of such an MLP on an image implicitly encodes the image within its weights. Beyond image representation, INRs have been successfully adopted for data compression (Strümpler et al.. 2022 K wan et al., (024)). (224).30 3D shape modeling (Park et al.) 2019 Mescheder al. 2019), novel-view synthesis with neural radiance fields (NeRF) (Mildenhall et al. | 2020), and burst fusion for denoising (Pearl et al., 2022) or layer separation of obstructions and background scenes (Nam et al. 2022
Chugunov et al. 2024).
LLike prior work we use the terms burst and multi-frame interchangeably Wronski et al.
2019
We note that the neural fields is used differently in computational neuroscience (A Aman 1977
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The common unsupervised way solve the MISR problem is to map the series of LR frames to a HR image, for example using steerable kernel regression (Wronski et al. 2019 Lafenetre et al, 2023). Instead of using the LR frames as input super-resolution work by De Lutio et al. (2019) and turn the problem formulation upside down and treat the LR frames as reconstruction targets. While Nam al. (2022) have explored such directions for burst fusion and layer separation tasks, their method was not designed to accurately solve sub- pixel frame alignment, which we show is crucial for MISR. Here, we build on these great ideas and design INRs dedicated for the MISR task. By directly parameterizing the affine transformations for the frame alignment and by introducing supersampling strategy, we improve the sub-pixel alignment and consequently the MISR performance.
model. we draw inspiration from the guided
We empirically validate the proposed SuperF algorithm on bursts obtained from satellite imagery as well as ground-level images from handheld cameras. In both cases, Superf gave compelling results. A key aspect of our approach is that it TTO method that avoids the need for large amounts of high-resolution training data. This also minimizes the risk of hallucinating high-resolution struc- tures, as opposed to supervised learning based approaches. Our contributions are summarized as:
1. We propose SuperF, a test-time optimization method for MISR based on implicit neural representations. We demonstrate that jointly optimizing the sub- sub-pixel frame alignment with an MLP shared across frames is both simple and key to adopt INRs to the MISR task.
2. Our method yields an improved sub-pixel alignment and continuous representation of the high-resolution signal, by directly parameterizing the affine transformations and by opti- mizing the INR with a supersampling strategy.
3. We introduce SatSynthBurst, a synthetic that our proposed approach generalizes to different domains including ground-level bursts from handheld cameras and satellite image bursts, and is robust to noise in real data.
satellite burst dataset for MISR research and show
2 RELATED WORK
2.1 MULTI-IMAGE RESEOLTIIOO (MISR)
Existing MISR approaches contain both learning-free and learning-based -baed methods. They are less prone to hallucinate structures compared to SISR. Test-time optimization (TTO) is applied to exploit natural hand tremors in handheld smartphone photography to capture bursts of slightly shifted raw images. Wronski et al. (2019) propose a steerable kernel regression that enables the direct RGB reconstruction without explicit demosaicing and improving resolution and signal-to-noise ratio, technology built into the 'pixel' phone. This approach was later reimplemented and adapted for satellite burst applications (Lafenetre et al. 2023).
Like SISR approaches that aim to learn priors from large training datasets, the MISR problem has also been approached with both supervised (Bhat et al. 2021a by Cornebise et al. 2022 and self-supervised (Nguyen et al.] (022) learning. Deep neural network architectures for burst super- resolution were proposed learn the alignment of multiple noisy RAW inputs in latent space via optical flow and the fusion with attention-based modules (Bhat et al. 2021a).. [Bhtt et al. (202lb) proposed a deep reparameterization of the MISR problem and formulated the reconstruction objec- tive in a learned latent space.
In this work, we propose a TTO approach leveraging the continuous nature of INR by jointly op- timizing the aligmment of low-resoloe oow-resouution frames in a continuous coordinate space. Hence, our ap- proach does neither require any high-resolution training data, nor a preprocessing step to register the LR frames. We compare our results with the approach proposed by Lafenetre et al. (2023). which the closest state-of-the-a thttt-t TTO approach and, at the same time, the only publicly available im- plementation. Since their high-resolution test data is not publicly available, we compare results on two different datasets. A handheld burst dataset (Bhat et al. 2021a) and a new synthetic satellite image burst dataset based open high resolution images (Cornebise et al., 2022). As opposed to prior work that focuses on one domain, we demonstrate that our approach generalizes to different domains including satellite and ground-level image bursts.
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2.2 IMPLICIT NEURAL REPRESENTATIONS (INR)
Recent advances in INRs have demonstrated the strength of representing continuous signals across various tasks (Essakine et al. 2025). but the development of INRs has mainly been driven by 3D
shape modeling (Park et al., 2019| Mescheder et al. 2019) and novel-view synthesis (Mildenhall
al. 2020p. These techniques have been adopted for multi-view satellite data (Derksen & Izzo,
202
Xiangli al. 2022), species distribution modeling (Cole et al., 2023), and medical imaging to c.g. model 3D MIR volumes (Wu et al. 2021
Cao jet al.) 2023: Chen et al., 2023] Zhu et al., 2025). Notably, Chen et al. (2021) propose the Local Implicit Image Function (LIIF) that models RGB values at arbitrary scaling factors. They devised a supervised learning approach that combines the explicit representation from a learned embedding
Recently INRs have been studied for single-image SR at arbitrary-scales (Chen al. 202
with local INR that is anchored in the nearest neighbor embeddings. Extending along this line of work, Becker et al. (2025) propose Thera, a neural heat field that explicitly models the point spread function (PSF) enable analytically correct anti anti-aliasing at any resolution.
Here we bring forward an approach to leverage the continuous characteristics of INRs for multi- image SR. As opposed prior work INR for SISR, we do not investigate a supervised approach. Since it is challenging to build training datasets for multi-image super-resolution, we propose a TTO-based solution that does not require any high-resolution training data, but optimizes an INR on multiple shifted LR frames. Key to our proposed approach is the joint optimization of the INR with the alignment of the LR frames, which allows us to share an INR across frames leading to a continuous representation of the underlying high-resolution signal.
Closest to our work the NIR approach presented by Nam et al. (2022). Although originally devel- oped to fuse bursts for layer separation, NIR also serves an INR baseline for the MISR task. Our method differs three components. First, while NIR estimates transformation matrices T, = g(l) using a separate ReLU MLP g conditioned the frame index t, we directly parametrize the trans- formation matrices as part of the model. Second, to improve sub-pixel alignment, we introduce a supersampling strategy to optimize the model
high-resolution coordinate grid that is subse- quently downsampled for supervision with the LR frames (similar strategies have been proposed to enhance details in novel view synthesis (Wang al., (022)). Finally, following prior MISR work Wronski et al. 2019), rather than estimating transformations for all frames, we use the base frame as the reference coordinate system to relatively align all other LR frames. This reduces the degrees of freedom and facilitates evaluation with high-resolution reference data by avoiding misalignment.
METHODOLOGY
We describe images by functions [0, 1)d - Th mapping coordinates to intensities. In our appli- cation, we consider two-dimensional RGB frames in homogeneous coordinates, i.e., d = 3 and (1)
ne = 3. Our input are T low-resolution frames YLR ......i. ViR in discretized form, i.e., we are given the values
finite discrete of points W [0, 1)d Our goal is find an approximation ÿHR of the underlying high-resolution signal YHR at points V c 10, Typically, V and W are grid (A) points and | |W| because the yiR are sampled with lower resolution than the target resolution defined by V.
Our approach is based on the assumption that y0l (v) R oo YuR (A ()), where A ( is affine transformation matrix and y boxcar filter. Convolution with the boxcar filter implements a spatial average pooling. The affine transformation matrix models misalignments by rotation and translation in the homogeneous coordinate system. In contrast to standard registration methods, our goal is also exploit misalignments by sub-pixel shifts, i.e., smaller than l|w; w for any w,, Wj E W.
3.1 IMPLICIT NEURAL REPRESENTATION (INR) SHARED ACROSS FRAMES
To optimize implicit representation of an image, make of coordinate- based multi-layer perceptron (MLP). The MLP model is denoted by fo with learnable parameters 0. It is optimized to output the intensities y (e.g., RGB pixel values) for the corresponding input coordinate E [0, 1)
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To share fo for T shifted low-resolution frames, need to align them sub-pixel scale. To achieve this, we make use of the continuous nature of INRs and optimize the parameters of affine transformation matrices A (4) that are applied to transform the input coordinates for each frame t. Following prior work (Wronski al. 2019),
the base frame as the reference coordinate system and set A I, where I the identity matrix (see Fig. 1 The coordinates v correspond to the high-resolution grid of the base frame:
80 (v) - (fo(A()))
(I)
The transformation matrices ( directly parameterized by two translation parameters Az(!)
and Ay(*) well as one rotation angle (O)) for each frame. In contrast, Nam et al. (022) proposed to estimate transformation matrices with another MLP for burst fusion. Since we only assume an approximate relationship between LR frames and expect some variation in brightness and contrast, our model optimizes frame specific spectral projection ((() with scale and shift parameter per spectral band. For the base frame this projection p² also fixed (scale and shift 0).
3.2 OPTIMIZATION WITH LOW-RESOLUTION FRAMES
We propose supersampling strategy to improve the sub-pixel alignment and consequently the im- plicit neural representation of the HR signal. During optimization, we run the INR at the high- resolution grid corresponding to the resolution of the super-resolved output. Since we only have the YLR available for the optimization, we need to match the output of the INR to the low-resolution frames. That is, we want to find 0 and Á (1) such that the low-resolution estimates
(1) LR. (v) +p ( (Jo(A ())
equal the low-resolution targets YL (v) on v E W. We fix the boxcar filter y, which implied by different resolutions of the discretized HR output and the given LR images. Ultimately, we optimize for multiple low-resolution frames by averaging a point-wise loss across the T frames:
T
arg min L(0, A
A = E
Σ e (FIR (1) I=1 NEW
In practice the convolution with the boxcar filter and the sampling at grid points W is simply implemented by an average pooling. We use MLPs with ReLU activation functions and stochastic gradient descent with mini batches of frames.
3.3 UNCERTAINTY ESTIMATION
To account for uncertainty in the LR frame targets, we model heteroscedastic noise, that is, pixel- wise uncertainty in the LR targets (Nix & Weigend, 1994). In addition to the HR RGB bands, we let the MI. decoder output band-specific uncertainty estimate per LR frame, i.e. T x ne additional outputs. Hence, the total number of outputs returned by the final layer of the MLP equals (T 1) x ne. This uncertainty output $(1) (v) interpreted as the logarithm of the variance of Gaussian random variable centered on the predicted HR signal. Taking the variance estimate into account, optimizing the (logarithmic) likelihood leads to the common loss function:
$12(0) + F YLR (()
(0)
(c)
LENLI. Σ
exp($(R(())
(1)
which is referred to as Gaussian negative log-likelihood (GNLL) loss. For locations where the model cannot minimize the squared reconstruction loss, LGNLI. can further be minimized by increasing the estimated variance. The first term acts as a regularizer and avoids arbitrarily high variance estimates. Both MSE and GNLL are derived under the assumptions that the inputs are independent and that the output has Gaussian noise with constant variance for MSE and varying variance for GNLL, respectively[ By switching from MSE to GNLL, we allow the model to minimize the loss by increasing the variance in noisy pixels, instead of forcing minimize the reconstruction error.
*Optimizing MSE is special case of optimizing GNLL with constant variance.
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3.4 INPUT TRANSFORMS FOR HIGH RESOLUTION REPRESENTATIONS
Since only optimize the model on low-resolution 'views' of the underlying high-resolution signal, the MLP is prone to output only the cowffrequencies of the signal. Hence, to recover high- frequencies captured by the multiple LR frames, we need to steer the ML.P to output high-frequency details. In general, coordinate-base reconstruction of low-frequency components of the target signal, whereas high-frequency details emerge only slowly during the convergence of optimization. Several approaches have been proposed
MLPs exhibit a spectral bias. The networks prioritize the
overcome this spectral bias (Sitzmann et al.) 2020 Saragadam et al.) 2023). We rely the
commonly used Fourier features (Tancik et al. 2020) as positional encoding. The feature map
y [0, 1)d + 2m is based on a random set of sine and cosine basis functions:
7() (2 v), ...... cos b,, v), sin(2 sin....,,sn((rbb.a
(5)
Each by E IR4, o2),, where the scale o is hyperparameter controlling the range of the sampled frequencies. We show that this hyperparameter is sensitive to the domain (c.g., satellite images vs. ground-level burst images), but the same value performs well across all samples within domain
1, ,,...,,,,, m, is sampled from an isotropic multivariate Gaussian distribution
4 EXPERIMENTAL RESULTS AND DISCUSSION
4.1 DATASETS
Our experiments are based on datasets from two domains: remote sensing and handheld cameras (see examples in Fig. 2 First, we create synthetic burst dataset from high-resolution satellite images to study various characteristics and the sensitivity of our proposed approach. Second, we demonstrate that our SuperF' approach also generalizes ground-level bursts from handheld cameras.
SatSynthBurst (satellite imagery). To study MISR for satellite imagery bursts we constructed a synthetic burst dataset derived from 20 open high-resolution satellite images selected from the WorldStrat dataset (Cornebise et al., 2022) (see examples in Appendix). For each high-resolution sample, we generate 16 low-resolution frames with scale factors 2, and 8, by randomly sampling sub-pixel shifts. Our dataset provides one LR base frame that is spatially aligned with the HR test images, a missing feature of existing datasets. This framework allows to study the influence of different upsampling factors keeping the HR resolution fixed. Furthermore, it gives us control over the sub-pixel shifts, and noise intensity. Although our approach does not require the true misalignment parameters, they allow to monitor the optimization dynamics when estimating the alignment. To realistically simulate the image formation process, we use spectral variations and additive Gaussian noise in all experiments (if not further specified). We follow the best practices for generating synthetic super-resolution data to mimic the modulation transfer function (mtf) of the Sentinel-2 sensor described by Lanaras et al. 2018). Details in the Appendix section A.I
SyntheticBurst (ground-level imagery). To evaluate on handheld bursts of ground-level scenes, we make use of the SyntheticBurst data provided by BBat al. (2021a) and e.g. used by |Bhat et al.) (2021b). We select 50 out of the 300 provided ground level bursts that provide interesting high- resolution structures, i.e., we remove for example bursts that are crops of homogeneous areas such as building walls or skies. Each burst consists of 14 LR frames, originally To study different upsampling factors, we vary the HR output resolution by downsampling the HR reference images, but we keep the LR frames provided to avoid changing the underlying noise model. Since this dataset does not provide a base LR frame aligned with the HR test image, we run brute force postprocessing to improve the alignment of the predictions before computing the error metrics (see Appendix section A.3).
scale factor of x8.
Tancik et al. (2020) establish the relation between o² and the bandwidth of the neural tangent kernel mod- eling the resulting MLP. They argue that wider kernel supports the learning of high frequency components, but that too wide kemee can lead to aliasing artifacts. They conclude that the parameter is problem dependent and has to be tuned.

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4.2 EXPERIMENTAL SETUP
We follow standard practices in super-resolution and report Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM), and Learned Perceptual Image Patch Similarity (LPIPS) (using AlexNet), computed using the implementation by Bhat et al. (2021a). All exper- iments are implemented in PyTorch and executed on a single NVIDIA H100 GPU with 80 GB of VRAM (see table in the Appendix for detailed training time, speed, memory usage, and FLOPs). If not further specified, all experiments use the Adam W optimizer with a base learning rate of x 10-3, which is decayed to x 10 over 2000 iterations using cosine annealing schedule and batch size of frame.
During evaluation, a 16-pixel boundary is cropped from all sides to reduce edge artifacts. We addi- tionally apply color matching as post-processing step, following Bhat et al. (2021a), to correct for global color and intensity shifts between the reconstruction and the ground truth. The scale hyper- parameter of the Fourier feature positional encoding is set to 10 for the SatSynthBurst and to 3 for the SyntheticBurst dataset.
4.3 COMPARISON TO EXISTING TEST-TIME OPTIMIZATION APPROACHES
Baseline approaches. As we propose a TTO approach, we compare to a state-of-the-art TTO approach for MISR, a steerable kernel regression method by Lafenetre et al. (2023). which is an adapted version of the approach described by Wronski et al. (2019). We also compare to burst fusion approach by Nam et al. (202)) (named NIR) and adapt it as a MISR baseline. Although developed for burst fusion for layer separation tasks, it is related our method as it uses INR with a built-in frame alignment (as introduced in section (.2).. To study the effect of each proposed methodological component, we integrate the NIR approach our framework keep all other com- ponents, that are design choices, the same. Thus, for both our SuperF and NIR, we use i) the same INR encoder (i.e., Fourier features with a ReLU MLP instead of Siren), ii) an affine matrix (instead of homography). iii) the same batch optimization, and iv) the same frame- frame-specific spectral projec- tion. As proposed by Nam et al. (2022), we run NIR for up to 5k iterations. For reference, we also report the performance of a bilinear upsampling of the LR base frame.
Comparison results. We present quantitative results in Table I for upsampling factors x2, x4, x8 focusing on PSNR. Additional metrics including LPIPS and SSIM are provided in the Appendix Table [ We find that both existing approaches cannot outperform the bilinear baseline in terms of PSNR. However, Lafenetre et al. (2023) yields better LPIPS than bilinear upsampling for an up- sampling factor x4. While Lafenetre al. (2023) has been designed for MISR of satellite bursts for upsampling up to factor 2, the NIR approach by Nam et al. (2022) has not been explicitly de- signed for super-resolution, but for denoising and layer-separation at the original resolution of the LR frames. In contrast, GNLL loss. While on SyntheticBurst both losses perform on par, the GNLL loss consistently im- proves upon the MSE on SatSynthBurst The GNLL possibly allows the INR to be more robust against the spectral variation in this dataset, which is less pronounced in the ground-level bursts.
SuperF approach outperforms all baselines using both the MSE and
Qualitatively, the methods by both Lafenetre et al. 2023) and Nam al. 2022) seem to be able to smooth and hence denoise the ground-level bursts, but lead to overly smooth results (see Fig. 2 and Appendix Fig. 13 for upsampling factors x2, x4, x8). Furthermore,
observed that for some satellite scenes, NIR produces a constant output and collapses at the beginning of the optimization. Our proposed SuperF approach yields pleasing results that can deal with the high noise-level in the ground-level bursts and represent the high reghhurcoottion signal in satellite scenes.
4.4 ABLATION STUDIES AND SENSITIVITY ANALYSES
To understand the individual components of our proposed methodology, we evaluate the perfor- mance gradually turning on each component in Table 2 We start with using our implementation of the INR with just a single LR frame (first row), but compare the resulting high-resolution recon- struction. This base experiment corresponds to an INR without using i) the Fourier feature positional encoding (FF); ii) the multiple LR frames amulti-framed iii) the optimization of the alignment of the L.R frames (align);
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Table I: Comparison with TTO baselines. PSNR (1) for different upscaling factors. Note that the SarSy fixes the HR output resolution while SyntheticBurst fixes the resolution of the LR frames. Hence, as the upsampling factor increases, we only expect lower performance metries for BarSynthBusst. Experimental setup: upsampling factors x2, x4, x8, 16 LR frames. Standard deviation across samples is given in parentheses and the number of iterations square brackets.
SatSynthBust x4
SyntheticBurst
x2
x8
x2
x4
x8
Bilinear
34.69 (3.50)
29.71 (3,64)
26.62 (3.68)
27.66 (3.50)
26.12 (3.72)
25.44 (3.82)
Lafenetre et al.
2023
33.46 (3.62)
27.70 (3.79)
24.88 (3.71)
27.02 (3.29)
26.46 (3.05)
25.19 (2.97)
NIK (Nam et Bi 2022
[2k]
26.26 (3.91)
24.63 (4.41)
(3.79)
23.62 (4.43)
22.69 (4.41)
22.28 (4.40)
NIR (Nam el al 2022
[5k]
25.65 (5.82)
24.99 (4.12)
23.61 (2.97)
24.46 (4.31)
23.39 (4.32)
22,93 (4.33)
SuperF NISE (ourS) [2K]
36.73 (1.66)
32.94 (1.83)
28.87 (2.32)
29.38 (3.43)
27.90 (3.94)
27.08 (3.97)
Superl' GNLL (ours) [2k]
37.26 (2.30)
34.03 (2.71)
29.28 (3.21)
29.48 (3.76)
27.47 (4.18)
26.58 (4.18)
LR Sample
Bilinaar
Lafenetra
NIR
Ours (MSS)
HR. Referance
536
ZH 536
ZH 536
Figure 2: Qualitative comparison with upsampling factor x4. From left to right, we show: one low-resolution (LR) frame, bilinear upsampling, steerable kernel regression (Lafenetre al. 2023). NIR (Nam et al. 2022). our SuperF' approach, and the high-resolution (HR) reference. Samples are from SyntheticBurst (row 1,2) 2) and SatSynthBurst (row 3, 4). More results in Appendix Fig.
We confirm that the positional encoding is also a crucial aspect for INRs in the MISR setup. How- ever, optimization a single LR frame is not able to recover any high-resolution details and, in fact, performs similar to a bilinear upsampling when used with the FF encoding (comparing Table with Appendix 5). Next, evaluate the performance of optimizing shared INR multiple LR frames without optimizing their alignment (third row). Compared to optimizing with a single LR frame, this leads to an lower performance result of the sub-pixel shifts which blurs the signal. Only by optimizing the sub-pixel alignment together with the shared INR, our proposed approach is able to leverage the information in multiple LR frames, which leads to substantial im- provement in performance (fourth row). These results hold systematically for both domains, satellite images (SatSynthBurst) and ground-level bursts (SyntheticBurst)
Effeet of the proposed components. To understand which of the proposed components lead to an advancement over the closest method by Nam et al. (202)), we investigate the effect by turning each component and off individually in Table 3 We find that using direct parametrization of the affine transformation parameters, instead of using another MLP to estimate the transformation most crucial, followed by the supersampling strategy, reduce the sub-pixel alignment error and MISR performance. Fixing the base frame is also beneficial, but only when using our direct parametrization. Combined, all three components substantially improve super-resolution perfor- mance and reduce the sub-pixel alignment error (cuclidean distance).
Sensitivity analyses Our method mainly depends on one key hyperparameter, the scale of the Fourier features 2² as described in section 3.4. We show that algorithm is sensitive to this
8

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Table Ablation studies. We study the importance of the individual components of our proposed approach. The base experiment (first row) corresponds to an INR without: i) the Fourier feature positional encoding (FF); ii) using multiple LR frames, i.e. single frame (multi-frame), iii) opti- mizing the alignment of the LR frames (align); Experimental setup: upsampling factor x4, 16 LR frames. Standard deviation across samples shown in parentheses.
SatSynth
SyntheticBurst
FF
multi-frame
align
PSNR
SSIM f
LPIPS
PSNR
SSIM 1
LPIPS
X
20.33 (2.16)
0.337 (0.160)
0.661 (0.050)
16.63 (2.91)
0.225 (0.138)
0.720 (0.042)
X
X
30.42 (3.24)
0.774 (0.073)
0,361 (0.047)
24.69 (3.08)
0.546 (0.107)
0,573 (0.047)
x
28. 18.1110 (3.32)
0.663 120)
0.458 (0.051)
22.83 (3.81)
0.523 (0.153)
0.592 (0.050)
/
32.94 (1.83)
0.853 (0.025)
0.287 (0.035)
27.87 (3.92)
0.774 (0.102)
0.383 (0.070)
Table 3: Effect of the proposed components to advance the NIR baseline (Nam et al.
2022
on the SatSynthBurst dataset. The first row is the NIR baseline without any of our contributions. Variants incrementally add or remove: i) direct parameterization of T ("Direct T")), ii) optimizing with supersampling ("SS"), and iii) using fixed base frame ("FBF").
Method
Direct T
SS
FBF
PSNR
SSIM
LPIPS +
Align. Err. +
Iter.
NIR (Nam et al. 2022
X
X
x
24.63
0.539
0.595
0.650
2000
26.14
0.580
0.479
0.012
2000
X
/
x
24.76
0.482
0.593
0.079
2000
x
X
V
26.39
0.621
0.483
0.319
2000
x
/
/
24.76
0,482
0.593
1.324
2000
J
/
26.20
0.578
0.476
0.012
2000
31.30
0.818
0.295
0.012
2000
SuperF (ours)
32.94
0.853
0.287
0.012
2000
parameter in Appendix Fig. 7 and 8 and that the best Fourier feature scale depends on the domain.
For the satellite image bursts an optimal scale is 10 and for the ground-level bursts it is 3. However, the optimal setting does not depend on the loss and the same setting generalizes across samples in the same domain. Furthermore, the sensitivity to the number of LR frames is shown in the Appendix section C.2
4.5 RESULTS REAL SENTINEL-2 SATELLITE IMAGES
We demonstrate that our method can be applied to real-world satellite images from Sentinel-2 (see Fig. 3p. We use Sentinel-2 images available from an AWS STAC endpoin and use the cloud-free samples for super-resolution. These are real-world examples and are therefore affected by noise due to lighting variation, changing landcover (e.g. crops), or seasonal variations like snow cover. In scenarios where the noise is dominating, does not hold and further development is nceded to account for such high noise levels.
assumption of repeated observations of the same scene
Robustness to occlusions. To study robustness of approach for noisy satellite image time series where some LR frames are partially covered by clouds, we curated two subsets of the WorldStrat dataset (Cornebise bitter, with clean and noisy time series, respectively. On the bitter dataset, we find that the GNLL approach effectively ignores cloudy pixels (Appendix Fig. [0] and improves performance compared to the MSE loss (Appendix T For clean time series in sweet, both losses perform on par.
al.) (202)) using real Sentinel-2 images, WorldStrat-sweet and WorldStrat-
4.6 DISCUSSION
Our proposed MISR approach, which jointly optimizes the alignment of LR frames and a shared INR. exhibits several advantageous characteristics: i) While existing approaches require a pre-
fggithu..com wtw/ wtw.///mmmt///art-sccomm (accessed: 2025-11-01)
A demo app super-resolve any place Earth is available here: styhneegithub.io/sugg

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DITIM
B
A) Jackeonvilll Interchauge. USA
B) Gemassoaa T'hermosolar Plant, Spain
C) Angkor Wat temple, Cambodiu
D) Sult furms, Philippines
Figure 3: Qualitative examples using real satellite images. We demonstrate that our method can align and super-resolve real satellite images from the Sentinel-2 mission by upsampling factor of 5 using filtered time series from Sentinel-2. Depending on the cloud cover this leads to a varying number LR images retrieved within 3-5 months (number of images: A: 25, B:15, C:9, D:7).
alignment step, SuperF directly works on large shifts by optimizing the alignment in continuous coordinate space (see Appendix section ii) As TTO approach, there is no need for any high- resolution training data. This allows SuperF to be applied to new domains without any pretraining. However, some limitations exist.
Limitations. Runtime may limit certain applications. Although our compact MLP is fairly memory-efficient, the iterative optimization process takes several seconds in our experiments (see Appendix Table running non-optimized code). This may pose limitations for mobile device appli- cations, but is less critical for remote sensing scenarios and other scientific and medical applications. possible way to reduce the number of iterations needed may be to learn the initialization of the INR as shown by Tancik et al. (202T). Real-world data can be highly noisy. For instance, satel- lite imagery may also partially be affected by cloud cover and handheld ground-level bursts may depict changing scenes. We assume that the observations capture the same scene. Occlusions and other drastic changes between frames introduce noise, which requires further analyses. However, uncertainty estimation module may help to be robust to such noise (Appendix Fig. 10). Risk of overfilting increases when setting the Fourier features scale hyperparameter too high. While this parameter depends the domain, it is rather robust across samples within a domain (Appendix Fig. 7 In practice, this parameter can be tuned by using some high-resolution validation images as shown in Fig. 7 or via visual inspection (see Fig.(8), Our proposed methodology would allow to test alternative INR decoders that avoid positional encodings such as SIREN (Sitzmann et al., 2020) or WIRE (Saragadam et 2023
Impact on society. The ability to super-resolve publicly available satellite data like Sentinel-2 enables a vast range of applications anywhere on Earth. This approach can support efforts to address critical societal challenges such climate adaptation, biodiversity conservation, and food security, for example, by facilitating environmental monitoring of deforestation, tree cover, tree counting, and mapping agricultural fields. However, these technological advances also carry the potential for misuse, including in the context of geopolitical conflicts or resource exploitation.
5 CONCLUSION
We bring forward an approach to leverage the continuous characteristics of implicit neural repre- sentations for multi-image super-resolution. The key characteristic of SuperF is to jointly optimize the sub-pixel alignment multiple low-resolution frames while sharing an INR across all frames. SuperF improves upon existing INR-based burst fusion approaches by optimizing INRs with a di- rect parameterization of the affine transformations and using a supersampling strategy, which leads to improved mub-pixel alignment and thus MISR performance. As TTO method, SuperF does not require any high-resolution training data, which facilitates the applicability to new domains - e.g. any location Earth and minimizes the risk of hallucinating high-resolution structures.
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ACKNOWLEDGMENTS
This work was supported in part by the Pioneer Centre for AI, DNRF grant number PI and by the Global Wetland Center (grant number NNF230C0081089) from Novo Nordisk Foundation.
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A DATASET CREATION AND EVALUATION PROCEDURE
In this section we provide details on i) the downsampling of high-resolution satellite images to create synthetic bursts of slightly shifted low-resolution images and ii) the postprocessing needed for evaluating the predicted high-resolution images.
A.1 CREATION OF THE SATSYNTHBURS DATASET (SATELLITE IMAGERY)
We constructed a synthetic burst dataset derived from 20 open high-resolution satellite images se- lected from the WorldStrat dataset (Cornebise et al. 2022) (see examples in Fig. 4. The high- resolution images from Airbus SPOT 6/7 satellite with a ground sampling distance (GSD) of up 1.5 are published under a CC BY-NC 4.0 license which allows us to publicly redistribute our SatSyntBBurst datasets under the same license for non-commercial purposes. We aim to simu- late low-resolution images comparable to the Sentinel-2 mission, but at varying spatial resolutions allowing to study downsampling factors of 2, 4, and 8. To simulate variation in the imaging conditions that could occur between images captured over several weeks, we incorporate spectral augmentations and additive Gaussian noise. Additionally, (2188) for generating synthetic super-resolution data using the modulation transfer function (miy') of the Sentinel-2 sensor. Hence, before downsampling,
follow the work by Lanaras et al.
blur the high-resolution images with Gaussian filter of standard deviation = 1/8 pixels, which emulates the mif of Sentinel-2 and, thus, the effective point spread function (psf) which is described as psf = / -2 22 log(mit)) T2 This followed by an average pooling with a window size of
IR
(a) Without spectral augmentation
(b) With spectral augmentation
Figure 4: Examples of the SatSynthBurst dataset (factor x4). The top row shows the underlying high-resolution (HR) image. Below we show four slightly misaligned low-resolution (LR) frames.
A.2 POSTPROCESSING FOR EVALUATION
We follow common practice in evaluating MISR results and use spectral alignment proposed by Bhat et al. (2021a) to correct any spectral mismatch between the high-resolution prediction and the test image. Metrics like the PSNR and SSIM rather sensitive small misalignments, whereas LPIPS is more robust. Furthermore, we follow the evaluation protocol of Bhat et al. (202 and
hutp://cectiicemmmooooooiiiiccea accesssd:: 2025-05-20)
14

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HR
HR
12
HR
536 312
LBG
Figure 5: Examples of the SyntheticBurst dataset (factor x8). The top row shows the underlying high-resolution (HR) image. Below we show four slightly misaligned low-resolution (LR) frames.
mask buffer of 16 boundary pixels avoid the effect of any boundary artifacts in the dataset (specifically, the Synthetic Burst dataset).
A.3 EVALUATION ON SYNTHETICBURS" (GROUND-LEVEL IMAGERY)
Unlike our SatSynthBurst dataset, the SyntheticBurst dataset (Bhat al. 2021a) does not provide base frame which spatially aligned with the high-resolution test image (see examples Fig. (5). Thus, additional postprocessing step is needed, before predicted HR image can be evaluated on the given HR test image. Therefore, we employ a brute force spatial alignment strategy to align the predicted image with the test image using affine transformation consisting of rotation and spatial translation. Our strategy selects the optimal translation within a 4x4 pixel neighborhood and the optimal rotation angle within a range of [0, 4] degrees.
We have experimented with the alignment strategy presented by Bhat et al. (202 that uses trained PWC-Net (Sun et al. 2018) to estimate the optical flow from the prediction the reference test image. However, this led to artifacts in the warped prediction, which is why we chose the brute force postprocessing.
B IMPLEMENTATION DETAILS
We summarize the hyperparameter settings for both datasets in Table The only hyperparameter that differs between datasets is the Fourier feature scale.
C ADDITIONAL RESULTS
C.1 COMPARISON OF BASELINES WITH ADDITIONAL METRICS
We provide additional evaluation metrics including PSNR, SSIM, and LPIPS for the baseline com- parison in Table
15

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Table 4: Hyperparameter settings.
Hyperparameters
SatSynthBurst
SyntheticBurst
LR resolution
128 / 64 /2
48 96 192 / 384
HR resolution
256
Optimizer
AdamW
Learning rate sched.
Cosine annealing
Learning rate base
2 x 10-3
Learning rate min
10-6
Weight decay
0.05 (0.9, 0.999)
Adam |
Batch size
1 L.R frame per iteration
Training iterations
2000
Fourier feature scale (σ) positional encoding dim
10
3
256
INR decoder
MLP (4 layers, ReLU, dim=256)
Table 5: Comparison of test-time optimization methods. Ours uses Fourier feature with scale 10 for SatSynthBurst (satellite) and scale for SyntheticBurst (ground-level), Experimental setup: upsampling factor x4, 16 LR frames. Standard deviation across samples is given in parentheses and the number of iterations in square brackets.
SatSynthBurst SSIM
SyntheticBurst SSIM
PSNR
LPIPS
PSNR
LPIPS
Bilinear
29.71 (3.64)
0.746 104)
0.382 (0.043)
26.12 (3.72)
0.703 (0.121)
0.455 (0.077)
Lalenetre el al. 2023
27.70 (3.79)
0.680 (0. 130)
0.261 (0.055)
26.46 (3:05)
0.664 (0.121)
0.384 (0. 118)
NIK (Nam al. 2022
[2k]
24.63 (4.42)
0.539 (0.175)
0.595 (0.076)
22.69 (4.41)
0.576 (0.171)
0.616 (0.089)
NIR
Nam al.
[5k]
24.99 (4.13)
0.544 (0.167)
0.587 (0.082)
23.39 (4.32)
0.606 (0.165)
0.574 (0.090)
SuperF MSE [2k]]][2]]
32,94 (1.83)
0.853 (0.035)
0.287 (0.054)
27.90 (3.95)
0.774 (0.102)
0.385 (0.070)
C.2 SENSITIVITY TO THE NUMBER OF LR FRAMES
We study the sensitivity to the number of available LR frames Fig. 6 This is critical aspect for both application domains. Handheld bursts might be limited in the number of frames since the scene might change for long overall exposure times. Satellite imagery like Sentinel-2 are captured with revisit period of x5 days. We thus need to consider longer time windows obtain multi-frame satellite images. However, longer time windows may lead to changing appearance of the scene due to activity on the ground or seasonality, which will hinder MISR. Furthermore, cloud-free images may be scarce, depending on the geographic region.
For the SatSynthBurst dataset, we observe that the PSNR saturates with samples for the factor x2, but keeps increasing slightly when using 16 samples for the larger upsampling factors. In contrast, the PSNR for the ground-level bursts keeps improving with more frames even for the factor x2. Additional frames may help reduce the high noise level in the ground-level bursts.
C.3 SENSITIVITY TO THE FOURIER FEATURE SCALE PARAMETER
As shown in the main paper, our method is sensitive to the Fourier feature scale, and the optimal hyperparameter depends on the domain, i.e. satellite imagery and ground-level bursts. We show the qualitative effect of the different Fourier features scales in Fig. g Setting the scale too low leads wooohhnoh,,, whereas setting too high leads grainy artifacts. However, we find that single parameter setting performs well across samples within a domain. We use the optimal setting for upsampling factor for all experiments including factor and (see hyperparameter setting in Table 4
16

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Upsample
Upsample 4x
Upsample Bx
40
25
-5
35
PSM (olb)
PSNA (al0)
PSWR (c16)
25
25
Sanyettuur
Syrtratittnnt CALL
Syiiaicttnt CALL.OM
Syttneiitnnt CALLL con
16
16
Number of Samples
Number of Samples
Number Samples
Figure 6: Sensitivity to the number of LR frames. From left to right, report PSNR for upsam- pling factors 2, 4, and 8 by varying the number of LR frames on the horizontal axis.
(a) Upsample 2x
(b) Upsample 4x
(c) Upsample 8x
Figure 7: Sensitivity analysis of the Fourier feature scale. The optimal hyperparameter depends on the domain, i.e. satellite imagery (SatSynthBurst in blue) and ground-level bursts (SyntheticBurst in red) require different settings. However, the optimal setting is invariant to the loss. For Synthet- icBurst we see small difference between the upsampling factor experiments. However, we note that the two datasets differ in the strategy of creating different upsampling factors. The SyntheticBurst varies the HR output resolution with fixed resolution of the LR frames. Hence, the absolute output resolution may affect the optimal Fourier feature scale. In contrast, the SatSynthBurst dataset fixes the HR output resolution and varies the resolution of the LR frames.
== 1.0
== 3.0
0 5.0
== 10.0
0 = 20.0
536312
ZH-536312
ZHH 536
781535912
Figure 8: Effect of the Fourier feature scale for MSE (upsampling factor x4). The optimal hyperparameter depends on the domain, i.c. satellite imagery and ground-level bursts require differ- ent settings. Setting the scale too low leads to over-smoothing, whereas setting it too high leads to grainy artifacts.
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C.4 ALIGNING LARGE SHIFTS WITHOUT PREPROCESSING
While existing methods (rronki et al. 2019 Lafenetre et al. 2023) rely on a pre-alignment proce- dure to first reduce the misalignment to sub-pixe shifts, our method directly work on multi-pixel shifts. Although the PSNR drops consistently with increased shifts, when comparing the results of bursts with sub-pixel shifts against bursts with shifts up to 4 LR pixels (see Table 6.. our method keeps outperforming the baseline. However, our method breaks in the extreme case with upsam- pling factor 8, i.e. the shifts of LR pixels correspond to 32 pixels the high-resolution image of size x56 pixels (i.e., > 12% relative shift). Further investigation is needed to study if this issue could be resolved with different hyperparameter setting, egg. by increasing the number of iterations or the learning rate.
Table 6: Comparing sub-pixe with large misalignments (PSNR). We compare SuperF results on bursts with sub-pixel shifts, iec max shifts of 1.0 LR pixels, vs. bursts with large shifts up to 4.0 LR pixels. Experimental setup: upsampling factor x2, x4, x8; 16 LR frames. Standard deviation across samples shown in parentheses.
SatSynthBurst x4
x2
x8
Bilinear
34.73 (3.65)
29.81 (3.88)
26.83 (4.03)
max shift: 1.0 LR pixels
SuperF (ours)
39.93 (2.49)
35.50 (2.39)
29.49 (2.71)
max shift: 4.0 LR pixels
SuperF (ours)
38.24 (2.56)
31.49 (4.13)
18.28 (6.37)
C.5 RESULTS FOR REAL SATELLITE BURSTS FROM THE WORLDSTRAT DATASET.
We demonstrated that our method can be applied to real world satellite images from the publicly available Sentinel-2 satellite images. addition, we use 8 Sentinel-2 images included in the World- Strat (Cornebise et al., 2022) Kaggle dataset (see Fig. 9 Many of the time series included in the WorldStrat dataset are affect by noise due to lighting variation, partial cloud cover and cloud shad- ows, changing landcover (e.g. crops), or seasonal variations like snow cover. In these scenarios, our assumption of repeated observations of the same scene does not hold.
To investigate how to tackle these challenging scenarios, we curate two new subsets of the World- Strat dataset, namely WorldStrat-sweel and WorldStrat-biter The sweet dataset composed of clean 25 time series from the WorldStrat dataset that neither have any clouds nor strong variations. In contrast, the bitter dataset, contains 25 noisy time series that show varying levels of cloud cover- age and noise (see examples in Fig. 10).
To assess the effect of the real-world variability on reconstruction accuracy, we evaluate SuperF with both MSE and GNLL losses the WorldStrat-sweet and WorldStrat-bitter subsets. As shown in Table [7] the two subsets expose clear differences, while both losses perform similarly on the clean samples in the sweef subset, the GNLL loss provides consistent advantage the noisy bitter samples. This confirms that modeling uncertainty is beneficial in scenarios where our assumption of repeated, noise-free observations breaks down.
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Bilinear
Prediction
Figure 9: Qualitative results on real WorldStrat samples.
Table 7: WorldStrat-sweet and WorldStrat-bitter results. The sweer subset contains 25 clean time series and the bitter contains 25 noisy time series (e.g. cloud cover). We use the same hyper- parameters as for SatSynthBurst (see Table 4 and optimize for 2000 iterations. Standard deviation across samples is given in parentheses. For the bitter samples, the GNLL loss outperforms MSE. Hence, estimating the uncertainty makes SuperF more robust against noise in the image bursts (e.g. occlusions from clouds). For clean time series in sweer, both losses perform par.
Dataset
Method
PSNR
SSIM
LPIPS
SuperFF MSE
27.86 (3.65)
0.654 (0.151)
0.507 (0.049)
WorldStrat-sweet
SuperF GNLL
27.88 (3.73)
0.657 (0.152)
0.506 (0.051)
SuperF MSE
27.42 (4.54)
0.645 (0.186)
0.532 (0.053)
WorldStrat-bitter
SuperF GNLI
28.46 (4.94)
0.677 (0.182)
0.503 (0.063)
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(d)
Figure 10: Visualization of estimated uncertainty maps. Four examples from the WorldStrat- bitter dataset, each showing LRR frames (top row) and the corresponding estimated uncertainty maps (bottom row). The uncertainty maps highlight cloudy or inconsistent pixels, enabling the GNLL loss to downweight these during optimization.
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C.6 QUALITATIVE RESULTS FOR DIFFERENT UPSAMPLING FACTORS: x2, x4, x8
We provide additional qualitative comparisons for both satellite image and ground-level image bursts upsampling factor x2 (Fig. П... x4 (Fig. 12), and x8 (Fig. [3) We note that the two datasets differ in the strategy of creating versions with different upsampling factors. The SatSynthBurst dataset fixes the HR output resolution and varies the resolution of the LR frames. Hence, we expect lower performance metrics for SatSynthBurst as the upsampling factor increases. In contrast, the SyntheticBurst varies the HR output resolution with fixed resolution the LR frames. Thus, the metrics are not comparable across upsampling factors.
We find that for the satellite imagery, our results for the upsampling factor x8 start to become grainy. This may be result of overfitting with suboptimal hyperparameter setting for the Fourier feature scale.
Table 8: Benchmarking computational costs. Training time, speed, memory usage, and FLOPs across different upsampling factors and loss types on the SatSynthBurst dataset (64 64 pixels low- resolution images). Values are averaged over an optimization run of 2000 iterations on NVIDIA H100 Tensor Core GPU.
Loss
factor
Time/Iter (ms)
Iterls
Memory (MB)
FLOPs (G)
MSE
2x
2.57
389.49
186.9
19.40
MSE
4x
4.39
227.95
549.2
77.61
MSE
8x
11.92
83.92
1863.8
310.45
MSE
16x
41.16
21.30
7250.3
1241.78
GNLL
2x
3.40
293. 75
188.6
20.01
GNLI
4x
5.24
190.74
549.5
80.03
GNLI
8x
13.77
72.63
1864.1
320.11
GNII
16x
47.38
21.10
7252.1
1280.44
C.7
ANY PLACE ON EARTH (DEMO APP)
We developed an interactive demo that allows users to select an arbitrary location on Earth and generate super-resolved image using the SuperF technique (available the project page: sjy hne. imn.giithub..osuperff The demo first queries an open STAC catalog of Sentinel-2 images within the user-specified time range. Each candidate image is passed through the OmniCloudMash discard observations affected by cloud cover. From the remaining cloud-free images, SuperF opti- mizes single high-resolution reconstruction, using the earliest valid image the reference frame. The user selects both the geographic location and the time interval of interest. After processing, the demo displays the resulting super-resolved image alongside all Sentinel-2 images that contributed to the reconstruction.
D USE OF LARGE LANGUAGE MODELS
We used LLMs as search engines to support literature research and as coding assistants.
httm:///ett.saaacc......cmmmmm// (ccessss: 1125-11-18)
http://gtthh.ccmm///////////m//d (accessed:: 2025-11-18)
21

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LR Sample
Billnear
Lafenetre
NIR
Ours (MSE)
HR Reference
Figure 11: Qualitative comparison with upsampling factor x2. From left to right, we show: one low-resolution (LR) frame, bilinear upsampling, stcerable kemeel regression (Lafenetre al. (023), NIR (Nam et al. 2022), our SuperF approach, and the high-resolution (HR) reference.
22

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LR Sample
Billnear
Lafenetre
NIR
Ours (MSE)
HR Reference
Figure 12: Qualitative comparison with upsampling factor x4. From left to right, we show: one low-resolution (LR) frame, bilinear upsampling, stcerable kemnel regression (Lafenetre al. (023), NIR (Nam et al. 2022), our SuperF approach, and the high-resolution (HR) reference.
23

---

LR Sample
Billnear
Lafenetre
NIR
Ours (MSE)
HR Reference
Figure 13: Qualitative comparison with upsampling factor x8. From left to right, we show: one low-resolution (LR) frame, bilinear upsampling, stcerable kemnel regression (Lafenetre al. (023), NIR (Nam et al. 2022), our SuperF approach, and the high-resolution (HR) reference.
24


Reviews:
[{"review_id": "GGeSSo8Lqz", "reviewer": "Reviewer_qyd9", "summary": "This paper presents SuperF, a new method for improving multiple-input super resolution (MISR).\nSuperF uses coordinate-based neural networks that represents images as continuous signals rather than fixed pixels.\nIt performs test-time optimization and  does not require pre-trained high-resolution data.\nSuperF shares one neural representation across  T low-resolution (LR) frames and jointly optimizes both alignments and reconstruction.\n\nSuperF sbegins with T LR frames, each frame  defined on a finite set of points. \nThe method estimates the underlying signal at a denser set of points relative to  LR input frames.\nIt assumes that each LR  frame is a convolution of a boxcar filter withan affine transformation of the high-resolution (HR)  target.  \nTo merge multiple frames, the method aligns the LR frames at the sub-pixel level.\n\nSuperF achieve its goal by aligning the the LR frames using affine transformation while modeling the HR image as a continuous signal through the neural network.\nThe HR prediction is blurred with a boxcar filter and downsampled to match the LR resolution. \nThe optimization for SuperF focuses on adjusting both the neural network parameters and the affine transformations so that all the LR frames agree on the same HR signal.\n\nThis paper provides experimental result to support it claims.", "questions": "Please check my comments under the Weaknesses.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The paper is well organized and clearly presented. It provide sufficient information to understand the motivation of the work. It also provides adequate information about prior and related work. This help in establishing the originality of the work. The approach of this work as an test-time optimization also underscores the significance of the contribution. The method provides a solution to the need for resources-efficient methods deployment of machine learning methods, especially on resource-constrained hardware. Finally, the experiments are well designed, clearly presents, and supports the central claims of the paper. This reflects the overall quality of the paper.", "weaknesses": "1).  Algorithm Statement or Architecture Diagram: While this paper did a good job at explaining the components of SuperF, it does not provide enough information to understand how these components fit together, especially for the purpose of reproducibility. For example, Table 5 in the Appendix shows that there are two decoder networks (Fourier feature-based decoder and  uncertainty decoder). It is not clear how they come together as a singe model under the SuperF model architecture. Having an algorithm statement or a complete model architecture will improve the reproducibility and the potential impact of SuperF.\n\n2). MSE vs GNLL:  Lines 245-246 state that  you have used the GNLL instead of  mean squared error. What was the assumption on the parameters of the  underlying Gaussian distribution for the GNLL?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "0GX2ZRoe82", "reviewer": "Reviewer_hY6U", "summary": "The paper introduces SuperF, a test-time optimization framework for multi-image super-resolution (MISR) using implicit neural representations (INRs). It jointly optimizes a shared coordinate-based MLP and frame-specific affine alignments to reconstruct a high-resolution image from multiple low-resolution inputs. The approach requires no training data and is validated on both synthetic satellite and handheld burst datasets, demonstrating strong PSNR and SSIM improvements over prior TTO baselines.", "questions": "See weaknesses for details.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "SuperF is well-motivated, bridging the gap between INR-based image representation and multi-frame super-resolution. The joint optimization of alignment and representation is elegant and mathematically consistent. The experiments are thorough, covering domain generalization, ablations, and sensitivity analyses. The work also provides a new synthetic satellite burst dataset, adding clear community value.", "weaknesses": "1. The paper lacks direct visual or quantitative comparison with modern learning-based MISR networks (e.g., DeepBurstSR or Transformer variants), limiting practical benchmarking.\n2. The uncertainty decoder’s effect is minor and under-analyzed; more discussion or visualization would clarify its contribution.\n3. Runtime (several seconds per image) and computational cost are only briefly mentioned; profiling across resolutions would make claims about efficiency more credible.\n4. The sensitivity to Fourier feature scale is described, but a cross-domain auto-tuning or normalization strategy would strengthen robustness.\n5. The method assumes static scenes; discussion on handling dynamic or partially misaligned inputs (e.g., moving clouds, handheld motion) is needed for real-world applicability.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "OUC0AZOMFe", "reviewer": "Reviewer_gFfE", "summary": "This paper presents SuperF, a test-time optimization method for multi-image super-resolution (MISR) using implicit neural representations (INRs). It improves sub-pixel alignment of low-resolution frames without requiring high-resolution training data, avoiding \"hallucinated\" structures. SuperF outperforms existing methods on both satellite and ground-level images, offering a data-efficient solution for super-resolution.", "questions": "1.\tThe current approach assumes that all frames depict the same scene, but how does SuperF perform when there are significant changes between frames, such as moving objects or occlusions?\n2.\tWhile the method shows domain sensitivity, could there be an automatic or adaptive mechanism for adjusting the scale based on the input domain, thus reducing the need for domain-specific tuning?\n3.\tGiven that cloud cover can obscure parts of satellite images, how well does SuperF perform when parts of the scene are occluded or affected by noise, especially with respect to the uncertainty estimation?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The use of implicit neural representations (INRs) for multi-image super-resolution (MISR) is innovative, offering a novel approach that leverages sub-pixel alignment optimization. \nBy avoiding the need for high-resolution training data, SuperF is a practical solution for real-world applications, including satellite imagery and handheld cameras.\nThe approach generalizes well across different datasets without the need for retraining, demonstrating versatility in various contexts like remote sensing and environmental monitoring.", "weaknesses": "The iterative optimization process, although memory-efficient, can be time-consuming, which might limit its applicability in real-time or mobile scenarios. Moreover, the method's performance is somewhat dependent on the Fourier feature scale hyperparameter, which requires careful tuning for different domains.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "cQu8F0G3EU", "reviewer": "Reviewer_Cozv", "summary": "This paper proposed a SuperF, a test-time optimization method for multi-image super-resolution based on implicit neural representations. SuperF designs an improved sub-pixel alignment and continuous representation of the high-resolution signal based on INR. The experimental results demonstrated that proposed method achieve star-of-the-art performance.", "questions": "Which dataset’s results are shown in Figure 2. The detailed description should be provided.  \n\nWhy choose SatSynthBurst and SyntheticBurst datasets for evaluation? Why build SatSynthBurst from the WorldStrat dataset? Can the WorldStrat dataset be used as an evaluation dataset? Did the previous method also use the same configuration?\n\nIn Table 1 and Table 2, what does the value in parentheses mean? The detailed description should be presented in the caption of the Table. The complexity of the proposed method should be provided. \n\nWhy the proposed (MSE) and the proposed (GNLL) have different performance. GNLL-based model has the best results in most cases for the SatSynthBurst dataset. However, MSE-based model has the best results for the SatSynthBurst dataset and large margins. In Figure 5, this phenomenon also occurs. The reason should be provided. What do these results represent?\n\nWhy use two loss functions, i.e., mean squared error(MSE) and the Gaussian negative log-likelihood (GNLL)? Do previous methods also use two loss functions? \n\nThe author claims that SuperF is a test-time optimization method. How to demonstrate the test-time optimization for the proposed method? Relevant experiments and analysis should be provided\n\nWhy use 4 MLP layers in the INR decoder and 3 MLP layers in the Uncertainty decoder? Corresponding ablation studies should be provided for specific layers.\n\nThe compared methods, i.e., Nametal.(2022), Lafenetreetal.(2023), they were two years ago, the latest methods should be discussed and compared\n\nSome typos should be revised, such as the left quotation mark in line 018. Please review the entire manuscript.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "A lot of experiments demonstrate the effectiveness of the proposed method and its components. An INR-based method is proposed for multi-image super-resolution.", "weaknesses": "Some detailed descriptions and reasons for the proposed method should be provided. \n\nMore experimental results should be provided for comprehensive comparison. \n\nThe writing of the paper needs improvement.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)