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REVIEW 3 major objections 4 minor 31 references

Blind Underwater Image Restoration using Co-Operational Regressor Networks

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A pair of cooperating regressors—an apprentice that restores and a master that scores PSNR—outperforms the prior state of the art on underwater image restoration with about nine times fewer parameters.

desk verdict CoRe-Net's 0.38 dB SOTA gain over a transformer with 9x fewer parameters is plausible but rests on a single unreplicated run; the cooperative regressor idea itself is worth a serious look. read the letter →

arxiv 2412.03995 v1 pith:5P54JE2E submitted 2024-12-05 cs.CV cs.LGeess.IV

Ozer Can Devecioglu , Serkan Kiranyaz , Turker Ince , Moncef Gabbouj This is my paper · ORCID
classification cs.CVcs.LGeess.IV
keywords underwaterimagerestorationcooperativelearningCo-OperationalRegressorNetworksSelf-OrganizedOperationalNeuralPSNRregressionimage-to-imagetransformationLSUIdatasetreal-time
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

This paper tries to establish that a compact pair of cooperating regressor networks, CoRe-Nets, can restore degraded underwater images as well as or better than much larger deep models. The idea is to split the usual generator role: an Apprentice Regressor transforms the corrupted image, while a Master Regressor learns to predict the PSNR of that output and feeds the prediction back into the apprentice's loss, turning the training loop into a direct PSNR booster. On the benchmark LSUI dataset, the authors report 24.54 dB PSNR with 7.2 million parameters, edging out the 24.16 dB of a 65.6-million-parameter U-Shape Transformer. A second pass over the same image can improve visual color and sharpness even when the PSNR score drops, which the authors read as evidence that the dataset's manually selected references are not the ceiling for quality. A sympathetic reader would care because the architecture promises real-time, low-complexity restoration without sacrificing the leading quantitative result.

What carries the argument

The load-bearing object is the two-network loop: the Apprentice Regressor (AR), a residual U-Net with 7.2 million parameters built from Self-Organized Operational Neural Network (Self-ONN) layers, and the Master Regressor (MR), a small stack of operational and dense layers that regresses a normalized PSNR score. In a Self-ONN, each neuron replaces a fixed convolution with a Taylor-polynomial operator $\psi(w,x) = w_0 + w_1 x + \dots + w_Q x^Q$, where $Q$ controls the degree of nonlinearity; $Q=1$ recovers a conventional CNN. During training, the MR minimizes the L1 distance between its estimate and the true PSNR of the AR output, normalized by a target PSNR, and the AR minimizes a weighted sum of the MR feedback, the negative true PSNR, and focal frequency loss. This closed feedback loop is what the paper calls PSNR boosting.

What would settle it

On a synthetic test set rendered with known clean scenes and known water attenuation coefficients, measure CoRe-Net's restored PSNR and color error against the known clean images; if its margin over the U-Shape Transformer shrinks below statistical significance, or its color error exceeds the Transformer's, the claimed superiority is an artifact of the manually selected LSUI references rather than true scene recovery.

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Extended reading notes

Core claim

CoRe-Net's central discovery, on the authors' own terms, is that cooperation beats competition for this restoration task: two networks that improve each other's loss (rather than a generator and discriminator that fight) reach the highest reported PSNR on the LSUI test split, 24.54 dB, using only 7.2 million parameters. The Master Regressor is trained to output the PSNR between the apprentice's output and the target, with ground-truth pairs mapped to a normalized target of 1, and the Apprentice Regressor is trained with a loss that combines that feedback, the true PSNR, and focal frequency loss. The same Self-ONN backbone used for both networks lets each convolutional kernel be a learnable low-degree polynomial nonlinearity, which the paper argues gives the pair more expressive capacity per parameter than plain convolutions or the transformer baseline.

Load-bearing premise

The load-bearing premise is that the LSUI ground-truth images, created by running 18 restoration methods and having volunteers pick the best, are clean enough to serve as true references, because both the PSNR numbers and the Master Regressor's training feedback are anchored to them.

Editorial extensions

If this is right

  • A 7.2-million-parameter restorer beats the 65.6-million-parameter U-Shape Transformer by 0.38 dB on the LSUI test split, so the state of the art does not require a transformer-scale model.
  • Restoring a $256 \times 256 \times 3$ image takes about 6.1 ms on a single CPU, roughly 150 times faster than real-time, which makes the method plausible for low-power underwater vehicles.
  • Because the Master Regressor supplies a differentiable PSNR target, the same cooperative loop should transfer to any image restoration task where PSNR is the main metric.
  • A second pass through the trained AR improves perceived color and sharpness beyond the dataset's ground-truth images, suggesting the restored outputs could be used to augment or revise the LSUI reference set.

Reading between the lines

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

  • If the LSUI ground truths carry the residual green casts the authors demonstrate, the reported 24.54 dB advantage may partly measure agreement with a subjective proxy; a true head-to-head would need a no-reference perceptual evaluation or a physically synthesized test set.
  • The MR's input could be swapped from a PSNR regressor to a learned no-reference quality score, which would let CoRe-Net train on unpaired underwater images and avoid the dataset's biased references entirely.
  • The same cooperative schedule could be applied to other blind restoration problems named in the paper, such as night-time or misty images, where paired clean references are also scarce.
  • Since the second-pass outputs often look cleaner than the GT, a practical extension is a self-improving loop that uses the second-pass output as a soft target for further training, though the authors do not propose this.
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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 / 4 minor

Summary. The paper proposes Co-Operational Regressor Networks (CoRe-Net) for blind underwater image restoration. The architecture pairs an Apprentice Regressor (AR), a Self-ONN-based U-Net that performs the image-to-image transformation, with a Master Regressor (MR) that learns to regress the PSNR of the AR output and feeds this quality estimate back into the AR loss. The training objective also includes a direct PSNR term and a focal frequency loss. Experiments on the LSUI benchmark report a first-pass PSNR of 24.54 dB with 7.2 million parameters, compared with 24.16 dB for the 65.6-million-parameter U-Shape Transformer, together with same-backbone operational U-Net and operational GAN baselines. A second-pass variant is presented as producing visually better outputs than the ground truth despite a lower PSNR.

Significance. If the reported results are robust, the paper makes a useful contribution: the cooperative MR feedback mechanism is a plausible alternative to adversarial training, the same-backbone internal comparison (Op. U-Net and Op. GAN) helps isolate the effect of the MR, and the compact 7.2 M parameter model with publicly released code could be attractive for practical underwater restoration. However, the central state-of-the-art claim rests on a single unreplicated training run with a small numerical margin over the prior method, and the authors themselves acknowledge that the LSUI ground truth is a subjective, algorithm-selected proxy. Both issues need to be addressed before the paper's main conclusions are fully supported.

major comments (3)
  1. [Section III.B / III.C, Table 1] The central claim that CoRe-Net exceeds the U-Shape Transformer (24.54 dB vs. 24.16 dB) is supported by only a single number per method. The experimental setup uses batch size 1 and up to 5000 back-propagation iterations, and no seeds, repeated runs, error bars, or significance tests are reported. With a 0.38 dB margin, run-to-run and initialization variability can change the ranking, especially because the MR is trained jointly against a moving target during training. Please report the mean and standard deviation over multiple seeds (or equivalent repeated evaluations) and provide a paired statistical test or bootstrap confidence interval for the PSNR comparison.
  2. [Section II.B, Equation (6)] Equation (6) is ambiguous as printed. The notation ||MR(B), α/Target PSNR||_{L1} is not a standard L1 loss between a network output and a target; it should be written explicitly, e.g., L1(MR(B), α/Target_PSNR), with α defined in Eq. (5). In addition, the second term is written as ||MR(A), 1||_{L1}, but the surrounding text says that for the ground truth A_Truth the target is 1, so it is unclear whether the MR input is the original degraded image A or the ground truth A_Truth. Please clarify the exact inputs and targets for both MR terms. Finally, the sensitivity of the method to the user-defined Target PSNR = 40 dB should be discussed or experimentally probed, because this constant appears directly in the MR loss.
  3. [Section III.D] The claim that the two-pass CoRe-Net can 'improve the GT images' in the LSUI dataset is supported only by selected visual examples and by a mean PSNR of 20.57 dB that is about 4 dB lower than the first-pass value. Since the paper itself states that the LSUI GT images are only as good as the restoration method manually selected by volunteers, the assertion of visual superiority needs a quantitative perceptual evaluation, a user study, or established no-reference image-quality metrics. Without such evidence, the second-pass result should be framed as a qualitative observation rather than a demonstrated benchmark improvement.
minor comments (4)
  1. [Section III.E] The reported processing time of 6.1 ms per 256x256x3 image corresponds to roughly 164 frames per second, which is about 5.5 times faster than a 30 fps real-time requirement, not 'approximately 150 times faster than the real-time requirements' as stated. Please correct this calculation or clarify the assumed real-time rate.
  2. [Section II.B, Equation (4)] The notation max(X_i) is used for the dynamic range of the normalized images and is defined as 1 - (-1) = 2. This is not the maximum pixel amplitude, which would be 1, so using a distinct symbol such as MAX or R would avoid confusion with the standard PSNR definition.
  3. [References] Reference [3] appears to be a duplicate of reference [2] rather than a distinct source; please provide the correct citation or remove the duplicate entry.
  4. [Table 1] The complexity comparison reports only parameter counts. Since the paper emphasizes real-time suitability, reporting multiply-accumulate operations or measured inference time for the competing methods would make the efficiency claim more concrete.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the reported PSNR is computed on a held-out test split, and the PSNR terms in the training losses are standard optimization objectives, not test-time predictions.

full rationale

I walked the paper's derivation chain from the loss definitions (Eqs. 4-7) through the experimental setup and the reported results. The central quantitative claim is the first-pass PSNR of 24.54 dB on the LSUI test set. The paper explicitly partitions the dataset: 'The LSUI dataset is partitioned in to train and test sets as 90% and 10% respectively as in [1] for fair comparative evaluations.' The reported PSNR is therefore measured on held-out data, not on the training set. The AR loss in Eq. (7) contains a direct negative PSNR term and the MR loss in Eq. (6) regresses a normalized PSNR target; these are training objectives, and optimizing a metric during training while reporting it on a held-out test set is standard practice, not circularity. The MR is trained to predict PSNR, but Table 1 reports actual PSNR values computed between restored outputs and ground-truth references, not MR predictions. The paper's reliance on Self-ONN components cites prior works by the same authors, but these are published architectures with public implementations (e.g., FastONN) and are used as building blocks; the state-of-the-art claim is tested empirically against external baselines rather than derived from those citations. The acknowledged subjectivity of LSUI ground-truth images and the unsupported second-pass 'better than GT' visual claim are validity or benchmark-quality concerns, not circularity. I found no step where a prediction or result is equivalent to its inputs by construction.

Assumptions & free parameters 4 free parameters · 3 assumptions · 1 invented entities

The central empirical result depends on the LSUI reference set, on PSNR as the quality metric, and on a handful of hand-set loss coefficients. No externally verified code or data artifacts were available in the review package, so the ledger reflects assumptions stated in the manuscript text.

free parameters (4)
  • Loss coefficient epsilon = 3
    Empirically set in Eq. (7); weights the MR feedback term in the Apprentice Regressor loss.
  • Loss coefficient beta = 0.05
    Empirically set in Eq. (7); weights the direct PSNR loss term.
  • Loss coefficient phi = 100
    Empirically set in Eq. (7); weights the focal frequency loss term.
  • Target PSNR = 40 dB
    User-defined normalization target for the Master Regressor in Eq. (6); affects MR training targets and therefore the feedback signal.
assumptions (3)
  • domain assumption LSUI ground truth images are valid references for restoration quality.
    The GT set is constructed by an ensemble of 18 enhancement methods plus volunteer selection (Section III.A). The paper itself admits GT images may contain artifacts (Section III.D), yet PSNR against GT is the primary evaluation and training target.
  • domain assumption PSNR is the primary measure of restoration quality.
    The method optimizes PSNR and reports it as SOTA, but the 2-pass result with lower PSNR is claimed to be visually superior, which undercuts PSNR as the sole quality metric.
  • standard math Taylor expansion approximation in Eq. (1)-(2) is valid for Self-ONN nodal operators.
    The method relies on representing nonlinear nodal operators as Taylor polynomials near zero; this is background theory from references [10] and [11].
invented entities (1)
  • Master Regressor (MR)
    purpose: Auxiliary network that regresses the PSNR of Apprentice Regressor outputs and feeds this estimate into the AR loss during training.
    MR is introduced in this paper. Its contribution is supported only by an internal comparison against Op. U-Net and Op. GAN, not by an external benchmark or an ablation that isolates MR from the direct PSNR loss term.

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Cite this review

Pith. "Pith review of Blind Underwater Image Restoration using Co-Operational Regressor Networks." pith.science (2026). https://pith.science/paper/5P54JE2E

@misc{pith2026241203995,
  author       = {Pith},
  title        = {Pith review of: Blind Underwater Image Restoration using Co-Operational Regressor Networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5P54JE2E}},
  note         = {Machine review of arXiv:2412.03995}
}
read the original abstract

The exploration of underwater environments is essential for applications such as biological research, archaeology, and infrastructure maintenanceHowever, underwater imaging is challenging due to the waters unique properties, including scattering, absorption, color distortion, and reduced visibility. To address such visual degradations, a variety of approaches have been proposed covering from basic signal processing methods to deep learning models; however, none of them has proven to be consistently successful. In this paper, we propose a novel machine learning model, Co-Operational Regressor Networks (CoRe-Nets), designed to achieve the best possible underwater image restoration. A CoRe-Net consists of two co-operating networks: the Apprentice Regressor (AR), responsible for image transformation, and the Master Regressor (MR), which evaluates the Peak Signal-to-Noise Ratio (PSNR) of the images generated by the AR and feeds it back to AR. CoRe-Nets are built on Self-Organized Operational Neural Networks (Self-ONNs), which offer a superior learning capability by modulating nonlinearity in kernel transformations. The effectiveness of the proposed model is demonstrated on the benchmark Large Scale Underwater Image (LSUI) dataset. Leveraging the joint learning capabilities of the two cooperating networks, the proposed model achieves the state-of-art restoration performance with significantly reduced computational complexity and often presents such results that can even surpass the visual quality of the ground truth with a 2-pass application. Our results and the optimized PyTorch implementation of the proposed approach are now publicly shared on GitHub.

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