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REVIEW 3 major objections 6 minor 33 references

Towards Lensless Image Deblurring with Prior-Embedded Implicit Neural Representations in the Low-Data Regime

T0 review · 3 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read An untrained SIREN with a PSF-informed loss outperforms low-shot lensless deblurring methods.

desk verdict New combination of INR and known-PSF untrained optimization for lensless deblurring, but the synthetic same-model evaluation leaves the claimed margin unproven. read the letter →

arxiv 2411.18189 v1 pith:QJO7DHI3 submitted 2024-11-27 eess.IV cs.CV

Abeer Banerjee , Sanjay Singh This is my paper · ORCID
classification eess.IVcs.CV
keywords lenslessimagingimplicitneuralrepresentationsuntrainednetworksimagedeblurringpriorembeddinglow-dataregimepointspreadfunctionunder-parameterization
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper tries to establish that implicit neural representations—coordinate networks that map pixel positions to color—can solve lensless image deblurring without any dataset training. Its central claim is that an untrained SIREN, optimized only against a physics-informed loss that convolves the network output with the known point-spread function, reconstructs lensless images with higher PSNR and SSIM than established untrained and low-shot alternatives. A second claim is that warm-starting the network by fitting it to a single image from the same domain, called prior embedding, speeds convergence and improves quality beyond a 10-shot domain-restricted method. If these claims hold, lensless cameras could be computationally deblurred with a compact network and a known PSF, without collecting paired training data or retraining for each camera.

What carries the argument

The central object is a SIREN, an MLP with sinusoidal activations that maps continuous coordinates $(u,v)$ to RGB values, kept under-parameterized relative to the $256 \times 256 \times 3$ image space. The mechanism that carries the argument is the physics-informed forward loss: at every optimization step the network's intermediate image is convolved with the known DiffuserCam PSF using FFT convolution, small Gaussian noise is added, and the error against the observed lensless image is backpropagated. Prior embedding is the second mechanism: before inverse optimization, the network is trained to fit one image from the target domain, producing a weight initialization that accelerates the subsequent PSF-informed reconstruction. The Under-Parameterization Ratio, defined as image-space dimensionality divided by network parameter count, supplies the comparison metric across architectures.

What would settle it

Apply the same untrained SIREN to real lensless captures from a DiffuserCam-style camera with a calibrated PSF and compare against a sharp reference; if the margin over the Deep Decoder shrinks or reverses under PSF mismatch or real sensor noise, the claimed superiority depends on the exact forward model.

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Extended reading notes

Core claim

On its own terms, the paper's discovery is that the inductive bias of a sinusoidal coordinate network is enough to turn a lensless measurement back into a clean image when the PSF is known: the network's output is convolved with the PSF in the Fourier domain and compared to the measurement, and that loss alone drives reconstruction. The authors report that this untrained SIREN outperforms the modified Deep Decoder at matched parameter counts, and that embedding a single domain image into the network's weights before optimization outperforms a 10-shot decoder baseline. They also introduce the Under-Parameterization Ratio to quantify how far below image dimensionality a network operates, and show that reconstructions improve as UPR decreases toward 1.

Load-bearing premise

The evaluation assumes the FFT-convolution forward model with the known DiffuserCam PSF and small Gaussian noise exactly generates the test measurements, because those measurements were synthesized by that same model.

Editorial extensions

If this is right

  • A roughly 132k-parameter SIREN can reconstruct 256x256 lensless images without paired training data, outperforming the untrained Deep Decoder at similar parameter counts.
  • Prior embedding from a single domain image gives faster convergence and better PSNR and SSIM than the 10-shot domain-restricted decoder baseline.
  • The Under-Parameterization Ratio provides a transferable way to compare untrained networks across architectures at matched under-parameterization.
  • Because the PSF is inside the loss, the same optimization procedure applies to any calibrated lensless camera by swapping the kernel, with no retraining.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper leaves untested the natural extension that a converged coordinate network can be sampled at arbitrary resolutions, since the INR is a continuous function rather than a pixel grid.
  • The monotone UPR-SSIM trend suggests a practical design rule: choose network width by sweeping UPR on synthetic examples before full optimization for a new PSF.
  • The evaluation never exposes the method to PSF mismatch or real sensor noise, so a testable next step is to add a calibration or mismatch-robust term before claiming real-world applicability.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper proposes an untrained implicit neural representation (SIREN) for lensless image deblurring. Reconstruction is performed by optimizing the INR to minimize the discrepancy between the PSF-convolved network output and the measured lensless image, with FFT-based convolution as the forward model. The method is extended with a prior-embedding step: the INR is first fit to a single domain-specific image and then used as the initialization for the physics-informed optimization. The authors report PSNR/SSIM improvements over Deep Decoder, ADMM, Learned-ADMM-UNet, and a 10-shot domain-restricted method on synthetic lensless images generated from the DiffuserCam PSF, and introduce the Under-Parameterization Ratio (UPR) to compare network sizes in the untrained regime.

Significance. If the reported results were validated under realistic lensless imaging conditions, the method would be a useful data-efficient alternative to GAN-based reconstructions, with the potential to adapt to new PSFs without retraining. The UPR metric is a simple and potentially useful tool for comparing under-parameterized network families. The paper includes thorough comparisons against several baselines and clear visualizations. However, the current evaluation is entirely based on synthetic measurements generated with the same forward model that is used inside the reconstruction loss, which severely limits the external validity of the central claim of superiority. The prior-embedded comparison is also confined to a single narrow domain, making the claimed generalization to the low-data regime insufficiently supported.

major comments (3)
  1. [Sec. V-A, V-C; Eq. (14)] All quantitative evaluations are performed on synthetic lensless images created by convolving clean images with the same DiffuserCam PSF k and adding small Gaussian noise, which is exactly the forward model used in the reconstruction loss inside the optimization loop. The authors themselves note in Sec. IV-A (citing [29]) that the shift-invariant PSF assumption is physically inexact and error-prone. Under model mismatch, such as real sensor noise, PSF calibration error, or shift variance, an untrained network can fit artifacts of the assumed forward model, and the reported margin over Deep Decoder and ADMM may shrink or reverse. To substantiate the claim of 'superior performance by a significant margin' for practical lensless imaging, the paper needs at least one experiment with real DiffuserCam measurements or with a deliberately mismatched PSF (e.g., synthesizing with a different PSF than the one used in the loss).
  2. [Sec. V-C; Fig. 6] The prior-embedded experiment uses a single microorganism image as the prior and a second microorganism image as the test target, both from the same narrow domain and dataset. This setup does not demonstrate that prior embedding provides a general advantage in the low-data regime; the improvement may largely reflect that the prior and target images are nearly identically distributed. The claim of 'bridging the gap between no-data and high-data regimes' (Abstract, Sec. VI) requires evaluation across multiple domains or at least on a more diverse test set, together with a sensitivity analysis with respect to the choice of the prior image (e.g., using an unrelated-domain prior or a degraded prior).
  3. [Sec. V-A; Table I and Fig. 3] The reported quantitative results are single-seed and given for fixed iteration counts, but the paper provides no analysis of sensitivity to the random initialization of the INR, the learning rate, the optimizer choice, or the Gaussian noise level in the forward model. Since the method is untrained and the entire reconstruction depends on the optimization trajectory, the absence of variance or statistical significance measures makes the claim of a 'significant margin' difficult to assess. The authors should report mean and standard deviation over multiple random seeds, or at least show that the ranking of methods is stable across hyperparameter choices.
minor comments (6)
  1. [Sec. IV-B, Eq. (17)] The notation ω(i)0 for the frequency scaling parameter of each SIREN layer is nonstandard; in the original SIREN paper, a single ω0 is used only in the first layer and subsequent layers use ω0=1. The authors should clarify whether they use a per-layer frequency scaling and how it affects initialization.
  2. [Algorithm 1 and Sec. IV-C] The loss function is described inconsistently: Algorithm 1 says 'L1 loss function', the text in Sec. IV-C says 'mean-squared error', Eq. (10) writes an L2 norm, and Fig. 1 says 'LMSE'. The exact loss used in all experiments should be stated unambiguously.
  3. [Sec. IV-D, Eq. (18)] The objective for prior embedding is written with malformed triple norms, and the subsequent equation 'θ∗ = arg min θ ||Mθ−y;Mprior||2 2' is not a well-formed optimization problem; the forward model k∗ and the initialization from Mprior should be stated explicitly.
  4. [Table I] The claimed trend 'increasing SSIM with decreasing UPR' is not strictly monotonic in the reported numbers (e.g., MDD at 10k iterations: UPR 1.47 gives 0.76, UPR 3.46 gives 0.73). The discussion should acknowledge this and avoid overstating the monotonicity.
  5. [Sec. V-C] The 'microorganism preprocessed images dataset [33]' is only cited as a Kaggle dataset; the exact dataset name, version, and any preprocessing steps should be provided for reproducibility.
  6. [Sec. I and II] The claim of being 'the first to leverage INRs for lensless image reconstruction' should be supported by a more exhaustive related-work search, since there may be concurrent or earlier works using implicit neural representations for lensless or coded-aperture imaging.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the claimed reconstruction is an untrained optimization against a PSF-informed forward loss, and the authors' self-citations appear only as baselines, not as load-bearing premises.

full rationale

The paper's central derivation is the physics-informed forward loss in Algorithm 1 and Eq. (10): an untrained SIREN maps coordinates to an image, the image is convolved with a known PSF via Eq. (14), and the network is updated against the measurement. The PSF and the measurement are inputs to this optimization, not outputs of a fitted model, so the reconstruction is not a renamed fit. The prior-embedded variant (Eq. 18) fits an INR to one domain-restricted image and uses it only as an initialization; the subsequent reconstruction is still driven by the forward loss and is therefore not statistically forced. The comparisons against the authors' prior methods [16] and [18] use those methods as baselines in quantitative and visual evaluations; no theorem or uniqueness claim from those papers is invoked to constrain the method, so self-citation is not load-bearing. The SIREN architecture and prior-embedding idea are attributed to external works [30] and [31]. The main substantive concern is external validity: quantitative tests are generated with the same FFT-convolution forward model used inside the reconstruction loop, and the authors themselves note that the shift-invariant PSF assumption is physically inexact (Sec. IV-A). That is a soundness or generalization limitation, not circular reasoning, because the solver and the test generator sharing an operator does not make the reported reconstruction equivalent to an input by construction. No step in the paper reduces a claimed prediction to a fitted parameter, a self-definition, or a renamed known result, so the appropriate circularity score is 0.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central performance claim rests on a closed simulation loop: the forward model in Eq. 13 is used inside the optimization loss and also to generate every test measurement. Therefore the shift-invariant known-PSF assumption, the untrained SIREN prior, and the manually tuned hyperparameters are load-bearing. No new physical entity is introduced; the only new metric is a descriptive ratio (UPR), not an entity.

free parameters (3)
  • SIREN architecture and training hyperparameters = 3 hidden layers, 208 nodes, UPR 1.49, steps 5000; learning rate and omega0 not reported
    The authors state they performed extensive hyperparameter tuning to finalize the network (Sec. IV), and the quantitative comparison uses these tuned values without reporting all of them.
  • Prior image for embedding = One image from microorganism dataset [33]
    Any single domain image could seed the network; the choice is not justified or varied, and it may affect the reported improvement.
  • Gaussian noise level in forward model = unspecified ('small amount')
    Noise added when simulating the lensless image during training is not quantified; it changes the optimization landscape and final PSNR/SSIM.
assumptions (5)
  • domain assumption Lensless image formation is modeled as shift-invariant convolution with a known PSF plus Gaussian noise (Eq. 13).
    Used throughout Algorithm 1 and Eq. 14; the authors explicitly note shift invariance is physically inexact (Sec. IV-A, citing [29]). All test data are generated with this same model, so model mismatch is not tested.
  • domain assumption The PSF is known exactly and available to the algorithm.
    Algorithm 1 requires k as input; no PSF calibration error or PSF mismatch experiments are reported, so robustness to imperfect PSFs is unknown.
  • domain assumption Untrained SIREN optimization acts as a natural image prior.
    The method inherits implicit regularization from SIREN periodic activations [30] and the untrained-optimization paradigm [13]; no proof or systematic sensitivity analysis is given.
  • domain assumption Prior embedding transfers from one domain image to another image in the same domain.
    The prior-embedded pipeline (Eq. 18) assumes fitting to one microorganism image yields an initialization that helps reconstruct a different image from the same domain; only a single demonstration is shown (Sec. V-C).
  • standard math FFT-based convolution in Eq. 14 is implemented with appropriate padding so it matches linear convolution of the PSF.
    The text specifies FFT convolution for speed but does not describe padding or boundary handling; if circular convolution is used, reconstructions at borders would be affected.

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Pith. "Pith review of Towards Lensless Image Deblurring with Prior-Embedded Implicit Neural Representations in the Low-Data Regime." pith.science (2026). https://pith.science/paper/QJO7DHI3

@misc{pith2026241118189,
  author       = {Pith},
  title        = {Pith review of: Towards Lensless Image Deblurring with Prior-Embedded Implicit Neural Representations in the Low-Data Regime},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QJO7DHI3}},
  note         = {Machine review of arXiv:2411.18189}
}
read the original abstract

The field of computational imaging has witnessed a promising paradigm shift with the emergence of untrained neural networks, offering novel solutions to inverse computational imaging problems. While existing techniques have demonstrated impressive results, they often operate either in the high-data regime, leveraging Generative Adversarial Networks (GANs) as image priors, or through untrained iterative reconstruction in a data-agnostic manner. This paper delves into lensless image reconstruction, a subset of computational imaging that replaces traditional lenses with computation, enabling the development of ultra-thin and lightweight imaging systems. To the best of our knowledge, we are the first to leverage implicit neural representations for lensless image deblurring, achieving reconstructions without the requirement of prior training. We perform prior-embedded untrained iterative optimization to enhance reconstruction performance and speed up convergence, effectively bridging the gap between the no-data and high-data regimes. Through a thorough comparative analysis encompassing various untrained and low-shot methods, including under-parameterized non-convolutional methods and domain-restricted low-shot methods, we showcase the superior performance of our approach by a significant margin.

Figures

Figures reproduced from arXiv: 2411.18189 by the authors.

Figure 1
Figure 1. The complete untrained iterative optimization procedure us [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. A. Prior-Embedding process: A domain-restricted image is represented using the INR simply by optimizing the MSE between the network output and the image. B. Prior-Embedded Physics-informed Inverse Imaging: The prior embedded INR Mprior is the starting point of the physics-informed optimization process that requires the PSF [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. PSNR versus iteration plots. The left plot depicts the results from the Deep Decoder framework, while the right plot shows the [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (4 more)
Figure 5
Figure 5. Figure 5: It is evident from the figure that, for a given UPR, [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 4
Figure 4. Figure 4: Visual comparison of reconstruction results of existing methods like the ADMM [1] in the extreme left column, followed by Le [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: Visual comparison of reconstruction results of our untrained INR against a modified Deep Decoder. The parameter count of the [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: Visual comparison of reconstruction results corresponding to [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]

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Reference graph

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