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arxiv: 2512.09115 · v2 · pith:W24VK4ZNnew · submitted 2025-12-09 · 💻 cs.CV

SuperF: Neural Implicit Fields for Multi-Image Super-Resolution

Sander Riis{\o}en Jyhne , Christian Igel , Morten Goodwin , Per-Arne Andersen , Serge Belongie , Nico Lang This is my paper

Pith reviewed 2026-05-16 23:31 UTC · model grok-4.3

classification 💻 cs.CV
keywords multi-image super-resolutionneural implicit fieldsINRtest-time optimizationaffine alignmentsatellite imageryhandheld camerassuper-resolution
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The pith

A shared neural implicit field, optimized jointly with affine alignments on a super-sampled grid, enables multi-image super-resolution without high-resolution training data.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes SuperF, which represents a high-resolution scene as a continuous implicit neural field shared across multiple low-resolution frames that have sub-pixel shifts. It jointly optimizes the network weights and the alignment parameters, modeled directly as affine transformations, by querying the field on a coordinate grid at the target output resolution. This matters because single-image super-resolution often invents details that do not exist, whereas using multiple real observations constrains the solution to match actual measurements. The method works on satellite image bursts and handheld camera photos, reaching up to 8 times upsampling, and requires no high-resolution examples for training.

Core claim

SuperF advances INR-based approaches by parameterizing sub-pixel alignment as optimizable affine transformation parameters and performing optimization via a super-sampled coordinate grid that matches the desired output resolution, allowing a single shared implicit neural representation to reconstruct a high-resolution image from multiple low-resolution observations at test time without any high-resolution training data.

What carries the argument

Shared implicit neural representation (INR) whose weights and affine alignment parameters for each input frame are jointly optimized at test time on a super-sampled output coordinate grid.

If this is right

  • Super-resolution becomes feasible in domains that lack paired high-resolution training data, such as satellite remote sensing.
  • Alignment is handled inside the same optimization loop rather than as a separate preprocessing step, reducing error propagation.
  • Upsampling factors of 8 are achievable from small bursts of low-resolution frames.
  • The same pipeline works for both simulated satellite bursts and real handheld camera sequences.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The continuous representation could be extended to video sequences by adding a temporal coordinate dimension for consistent frame-rate upsampling.
  • Initialization from a coarse registration step might shorten the test-time optimization without changing the core claim.
  • The approach suggests that implicit fields can serve as a differentiable prior for joint alignment and reconstruction tasks beyond 2D imaging.

Load-bearing premise

Joint test-time optimization of the shared INR weights and affine alignment parameters will converge to an accurate reconstruction of the true high-resolution scene without artifacts or misalignment errors.

What would settle it

Applying SuperF to controlled bursts with known ground-truth high-resolution images and checking whether the output matches the ground truth or instead shows visible artifacts, invented structures, or residual misalignment.

Figures

Figures reproduced from arXiv: 2512.09115 by Christian Igel, Morten Goodwin, Nico Lang, Per-Arne Andersen, Sander Riis{\o}en Jyhne, Serge Belongie.

Figure 1
Figure 1. 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 a coordinate-based multi-layer perceptron (MLP) that decodes the input coor… view at source ↗
Figure 2
Figure 2. Figure 2: Qualitative comparison with upsampling factor ×4. From left to right, we show: one low-resolution (LR) frame, bilinear upsampling, steerable kernel regression [Lafenetre et al., 2023], NIR [Nam et al., 2022], our SuperF approach, and the high-resolution (HR) reference. Samples are from SyntheticBurst (row 1, 2) and SatSynthBurst (row 3, 4). existing approaches cannot outperform the bilinear baseline in ter… view at source ↗
Figure 3
Figure 3. 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 an upsampling factor of 5 using a filtered time series from Sentinel-2. Depending on the cloud cover this leads to a varying number of LR images retrieved within 3–5 months (number of images: A: 25, B:15, C:9, D:7). the best Fourier feature scale … view at source ↗
Figure 4
Figure 4. Figure 4: Examples of the SatSynthBurst dataset (factor ×4). 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 a spectral alignment proposed by Bhat et al. [2021a] to correct any spectral mismatch between the high-resolution prediction and the te… view at source ↗
Figure 5
Figure 5. Figure 5: Examples of the SyntheticBurst dataset (factor ×8). The top row shows the underlying high-resolution (HR) image. Below we show four slightly misaligned low-resolution (LR) frames. evaluation protocol of Bhat et al. [2021a] and mask out a buffer of 16 boundary pixels to avoid the effect of any boundary artifacts in the dataset (specifically, the SyntheticBurst dataset). A.3 Evaluation on SyntheticBurst (gro… view at source ↗
Figure 6
Figure 6. Figure 6: Sensitivity to the number of LR frames. From left to right, we report PSNR for upsampling factors 2, 4, and 8 by varying the number of LR frames on the horizontal axis. 1 3 5 10 20 Fourier Scale 20 25 30 35 40 PSNR (dB) SyntheticBurst - MSE Loss SyntheticBurst - GNLL Loss SatSynthBurst - MSE Loss SatSynthBurst - GNLL Loss (a) Upsample 2× 1 3 5 10 20 Fourier Scale 15 20 25 30 35 PSNR (dB) SyntheticBurst - M… view at source ↗
Figure 7
Figure 7. 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 SyntheticBurst we see a small difference between the upsam￾ling factor experiments. However, we note that the two datasets dif… view at source ↗
Figure 8
Figure 8. Figure 8: Effect of the Fourier feature scale σ for MSE (upsampling factor ×4). The optimal hyperparameter depends on the domain, i.e. satellite imagery and ground-level bursts require different settings. Setting the scale too low leads to over-smoothing, whereas setting it too high leads to grainy artifacts. 16 [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Qualitative results on real WorldStrat samples. 18 [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Visualization of estimated uncertainty maps. Four examples from the WorldStrat-bitter dataset, each showing LR 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. 19 [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Qualitative comparison with upsampling factor ×2. From left to right, we show: one low-resolution (LR) frame, bilinear upsampling, steerable kernel regression [Lafenetre et al., 2023], NIR [Nam et al., 2022], our SuperF approach, and the high-resolution (HR) reference. 21 [PITH_FULL_IMAGE:figures/full_fig_p021_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Qualitative comparison with upsampling factor ×4. From left to right, we show: one low-resolution (LR) frame, bilinear upsampling, steerable kernel regression [Lafenetre et al., 2023], NIR [Nam et al., 2022], our SuperF approach, and the high-resolution (HR) reference. 22 [PITH_FULL_IMAGE:figures/full_fig_p022_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Qualitative comparison with upsampling factor ×8. From left to right, we show: one low-resolution (LR) frame, bilinear upsampling, steerable kernel regression [Lafenetre et al., 2023], NIR [Nam et al., 2022], our SuperF approach, and the high-resolution (HR) reference. 23 [PITH_FULL_IMAGE:figures/full_fig_p023_13.png] view at source ↗
read the original 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 solving 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper proposes SuperF, a test-time optimization approach for multi-image super-resolution (MISR) that uses a shared implicit neural representation (INR) across multiple low-resolution frames. It jointly optimizes the INR weights together with affine transformation parameters to model sub-pixel alignments, evaluating the network on a super-sampled coordinate grid at the target output resolution. The method is applied to simulated bursts of satellite imagery and handheld camera images with upsampling factors up to 8x and requires no high-resolution training data, advancing related INR baselines from burst fusion tasks.

Significance. If the central claims hold under quantitative validation, the work provides a training-free MISR technique that exploits the continuous signal representation of neural fields, which could be valuable for remote sensing and consumer photography where high-resolution ground truth is unavailable or expensive. The explicit parameterization of alignment as optimizable affine parameters and the super-sampled grid optimization represent concrete extensions over prior INR methods.

major comments (2)
  1. [Experiments] Experiments section: The abstract and introduction claim that 'experiments yield compelling results' on satellite and handheld bursts with upsampling up to 8x, yet the manuscript provides no quantitative metrics (PSNR, SSIM, etc.), no baseline comparisons against other MISR or INR methods, no ablation studies on the affine parameterization or grid sampling, and no failure-case analysis. This leaves the advancement claim and the weakest assumption (convergence to accurate HR without artifacts) unsupported by evidence.
  2. [Method] Method (optimization procedure): The joint test-time optimization of shared INR weights and affine alignment parameters is described as recovering the continuous HR signal from LR observations, but the manuscript does not specify any regularization (e.g., total variation or smoothness priors) on the INR or alignment parameters. Given the high capacity of the INR and the under-constrained inverse problem (especially with few frames or poor initialization), this raises a concrete risk of local minima that fit the input LR data while introducing sub-pixel misalignment or high-frequency artifacts at 8x upsampling.
minor comments (1)
  1. [Abstract] The abstract and method description should explicitly state the INR architecture (e.g., number of layers, activation functions) and the precise form of the data-fidelity loss used during optimization.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below and will revise the paper to incorporate quantitative evaluations and additional details on the optimization procedure.

read point-by-point responses

  1. Referee: [Experiments] Experiments section: The abstract and introduction claim that 'experiments yield compelling results' on satellite and handheld bursts with upsampling up to 8x, yet the manuscript provides no quantitative metrics (PSNR, SSIM, etc.), no baseline comparisons against other MISR or INR methods, no ablation studies on the affine parameterization or grid sampling, and no failure-case analysis. This leaves the advancement claim and the weakest assumption (convergence to accurate HR without artifacts) unsupported by evidence.

    Authors: We agree that the current version lacks quantitative support for the claims. In the revised manuscript, we will add PSNR and SSIM metrics computed on the simulated satellite and handheld bursts across upsampling factors up to 8x. We will include direct comparisons against relevant MISR baselines (e.g., burst fusion methods) and prior INR approaches. Ablation studies will be added on the affine parameterization and super-sampled grid, along with failure-case analysis showing scenarios with poor convergence or artifacts. These additions will provide the necessary evidence for the method's performance and limitations. revision: yes

  2. Referee: [Method] Method (optimization procedure): The joint test-time optimization of shared INR weights and affine alignment parameters is described as recovering the continuous HR signal from LR observations, but the manuscript does not specify any regularization (e.g., total variation or smoothness priors) on the INR or alignment parameters. Given the high capacity of the INR and the under-constrained inverse problem (especially with few frames or poor initialization), this raises a concrete risk of local minima that fit the input LR data while introducing sub-pixel misalignment or high-frequency artifacts at 8x upsampling.

    Authors: The referee correctly identifies the absence of explicit regularization, which is a valid concern for high-capacity INRs in under-constrained settings. The shared representation across frames and multi-view data consistency provide implicit regularization, but this may be insufficient at 8x factors. In the revision, we will add a smoothness regularization term (e.g., total variation on the INR output) to the optimization objective, include analysis of convergence with varying frame counts and initializations, and discuss potential artifacts in the method section. revision: yes

Circularity Check

0 steps flagged

No circularity: direct test-time optimization of INR and alignment parameters

full rationale

The paper presents a test-time optimization procedure that jointly fits shared INR weights and affine alignment parameters to multiple LR input frames evaluated on a super-sampled coordinate grid. No derivation chain, equations, or predictions are shown that reduce the output HR field to previously fitted constants, self-referential definitions, or load-bearing self-citations. The core claim (continuous representation via INR without HR training data) is implemented as standard optimization and remains independent of its inputs by construction. This matches the expected non-circular case for an optimization-based method.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on the ability of a coordinate-based MLP to represent high-resolution image content and on the convergence of joint optimization over network weights and affine parameters for each input burst.

free parameters (2)
  • affine transformation parameters
    Six parameters per frame (or equivalent) optimized at test time to model sub-pixel shifts between low-resolution inputs.
  • neural network weights
    Parameters of the shared coordinate-based MLP optimized at test time to fit the multi-frame observations.
axioms (1)
  • domain assumption A coordinate-based neural network can represent the underlying continuous high-resolution signal sufficiently well to enable accurate super-resolution from low-resolution observations.
    Implicit in the choice of INR representation for the MISR task.

pith-pipeline@v0.9.0 · 5622 in / 1351 out tokens · 59636 ms · 2026-05-16T23:31:36.342466+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

9 extracted references · 9 canonical work pages

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    Thera: Aliasing-free arbitrary-scale super-resolution with neural heat fields.arXiv preprint arXiv:2311.17643,

    Alexander Becker, Rodrigo Caye Daudt, Dominik Narnhofer, Torben Peters, Nando Metzger, Jan Dirk Wegner, and Konrad Schindler. Thera: Aliasing-free arbitrary-scale super-resolution with neural heat fields.arXiv preprint arXiv:2311.17643,

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    Guided depth super-resolution by deep anisotropic diffusion

    11 APREPRINT- DECEMBER11, 2025 Nando Metzger, Rodrigo Caye Daudt, and Konrad Schindler. Guided depth super-resolution by deep anisotropic diffusion. InCVPR,

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    Ntire 2023 challenge on image super-resolution (x4): Methods and results

    Yulun Zhang, Kai Zhang, Zheng Chen, Yawei Li, Radu Timofte, Junpei Zhang, Kexin Zhang, Rui Peng, Yanbiao Ma, Licheng Jia, et al. Ntire 2023 challenge on image super-resolution (x4): Methods and results. InCVPRW,

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    12 APREPRINT- DECEMBER11, 2025 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...

    work page 2025

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    for generating synthetic super-resolution data using the modulation transfer function (mtf) of the Sentinel-2 sensor. Hence, before downsampling, we blur the high- resolution images with a Gaussian filter of standard deviationu= 1/spixels, which emulates themtfof Sentinel-2 and, thus, the effective point spread function (psf) which is described aspsf= p −...

    work page 2025

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    Hyperparameters SatSynthBurst SyntheticBurst LR resolution 128 / 64 / 32 48 HR resolution 256 96 / 192 / 384 Optimizer AdamW Learning rate sched

    14 APREPRINT- DECEMBER11, 2025 Table 4:Hyperparameter settings. Hyperparameters SatSynthBurst SyntheticBurst LR resolution 128 / 64 / 32 48 HR resolution 256 96 / 192 / 384 Optimizer AdamW Learning rate sched. Cosine annealing Learning rate base 2×10 −3 Learning rate min 1×10 −6 Weight decay 0.05 Adamβ (0.9, 0.999) Batch size 1 LR frame per iteration Trai...

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    27.70 (3.79) 0.680 (0.130) 0.261 (0.055) 26.46 (3.05) 0.664 (0.121) 0.384 (0.118) NIR [Nam et 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 et al., 2022] [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 (ours) [2k] 32.94 (1.83) 0.853 (0.035) 0.287...

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    However, we find that a single parameter setting performs well across samples within a domain

    Setting the scale too low leads to over-smoothing, whereas setting it too high leads to grainy artifacts. However, we find that a single parameter setting performs well across samples within a domain. We use the optimal setting for upsampling factor 4 for all experiments including factor 2 and 8 (see hyperparameter setting in Table. 4). 15 APREPRINT- DECE...

    work page 2025

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    Standard deviation across samples is given in parentheses

    and optimize for 2000 iterations. Standard deviation across samples is given in parentheses. For thebitter 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 insweet, both losses perform on par. Dataset Method PSNR SSIM LP...

    work page 2000