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arxiv: 2605.24590 · v1 · pith:XHSPCFWUnew · submitted 2026-05-23 · 💻 cs.CV · cs.LG· stat.ML

Physen-Noise2Noise: Physics-Guided Self-Supervised Defocus Deblurring with Bias Correction under Low-Light Conditions

Ziyan Huang , Lang Wu , Hongji Wang , Yifei Liu , Dongliang Tang , Hongqiao Wang This is my paper

Pith reviewed 2026-06-30 13:11 UTC · model grok-4.3

classification 💻 cs.CV cs.LGstat.ML
keywords defocus deblurringself-supervised learninglow-light imagingnoise bias correctionphysics-guided deblurringmulti-frame reconstruction
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The pith

A physics-guided self-supervised method corrects biased noise in low-light defocus deblurring using frequency-domain constraints.

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

The paper introduces Physen-Noise2Noise, a framework for deblurring defocused images captured in low light with complex biased noise. It uses a physical model of defocus imaging to derive a frequency-domain constraint and incorporates it through a learnable noise bias parameter in a self-supervised setting with only noisy multi-frame inputs. This allows joint bias correction and detail recovery without needing clean reference images. The approach also includes a multi-frame initialization strategy and a pretrain-finetune variant for better performance. Experiments show it outperforms existing self-supervised methods on both simulated and real-world data.

Core claim

The central claim is that by deriving and incorporating a frequency-domain constraint from the defocus imaging process into a Noise2Noise framework via a learnable noise bias parameter, the method can effectively handle biased noise in low-light defocus deblurring, enabling high-quality reconstruction from noisy observations alone.

What carries the argument

The learnable noise bias parameter that encodes the frequency-domain constraint inherent to defocus imaging, allowing joint bias correction and deblurring in the self-supervised training.

If this is right

  • The method enables deblurring without clean ground truth images by using multi-frame noisy observations.
  • It provides a stable starting point for reconstruction through multi-frame noisy initialization.
  • A pretrain-finetune strategy enhances robustness under challenging noise conditions.
  • It outperforms state-of-the-art self-supervised approaches in the presence of complex biased noise.

Where Pith is reading between the lines

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

  • This approach could extend to other imaging degradations where physical models provide frequency constraints, such as motion blur.
  • Integrating the bias parameter might improve other self-supervised denoising tasks in computer vision.
  • Testing on more diverse real-world datasets could reveal limitations in generalization to varying noise distributions.

Load-bearing premise

The frequency-domain constraint inherent to the defocus imaging process can be effectively incorporated via a learnable noise bias parameter to enable joint bias correction and deblurring under realistic low-light conditions.

What would settle it

A direct comparison showing that removing the learnable noise bias parameter leads to significantly worse performance on datasets with known non-zero-mean noise would falsify the central claim.

Figures

Figures reproduced from arXiv: 2605.24590 by Dongliang Tang, Hongji Wang, Hongqiao Wang, Lang Wu, Yifei Liu, Ziyan Huang.

Figure 1
Figure 1. Figure 1: (a) Impact of the defocus blur frequency constraint on deblurring. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) The SN2N strategy: integration of noise-to-noise loss and self [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (a) Comparison of different methods on simulated data. (b) Ablation study on simulated data. (c) Performance comparison of PN2N under various [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a) Comparison of different methods on real experimental data. (b) Experimental setup and equipment for real-world validation. (c) A simple comparison [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a) illustrates the effect of the primary network learning rate on convergence and deblurring performance, while (b) shows the impact of the learnable bias [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: PSF used in the experiment. REFERENCES [1] S. Ai and J. Kwon, “Extreme low-light image enhancement for surveil￾lance cameras using attention u-net,” Sensors, vol. 20, no. 2, p. 495, 2020. [2] L. Qu, S. Zhao, Y. Huang, X. Ye, K. Wang, Y. Liu, X. Liu, H. Mao, G. Hu, W. Chen et al., “Self-inspired learning for denoising live-cell super-resolution microscopy,” Nature Methods, vol. 21, no. 10, pp. 1895– 1908, 2… view at source ↗
read the original abstract

Low-light, long-exposure defocus deblurring remains a challenging problem due to the simultaneous presence of severe blur and complex biased noise. Existing methods typically rely on simplified noise assumptions, which limits their effectiveness under realistic imaging conditions. In this work, we propose Physen-Noise2Noise, a self-supervised deblurring framework guided by the physical model of defocus imaging, which leverages noisy multi-frame observations without requiring clean reference images. Unlike conventional Noise2Noise-based approaches that assume zero-mean noise, we derive a frequency-domain constraint inherent to the defocus imaging process and incorporate it into the learning framework via a learnable noise bias parameter. In addition, a multi-frame noisy initialization strategy is introduced to suppress complex biased noise prior to deblurring, providing a more stable starting point for reconstruction. This formulation explicitly models biased noise and enables joint bias correction and high-frequency detail recovery during training. Furthermore, we develop a pretrain-finetune variant to enhance robustness and generalization under challenging noise conditions. Extensive experiments on both simulation and real-world datasets demonstrate that the proposed method consistently outperforms state-of-the-art self-supervised approaches for defocus deblurring in the presence of complex biased noise.

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 manuscript proposes Physen-Noise2Noise, a self-supervised framework for defocus deblurring under low-light conditions with complex biased noise. It leverages noisy multi-frame observations without clean references, derives a frequency-domain constraint from the defocus imaging model, and incorporates this constraint via a learnable noise bias parameter to enable joint bias correction and high-frequency detail recovery. The method also includes a multi-frame noisy initialization strategy and a pretrain-finetune variant. Extensive experiments on simulated and real-world datasets are reported to show consistent outperformance over state-of-the-art self-supervised defocus deblurring approaches.

Significance. If the frequency-domain constraint is shown to be independent of the fitted bias parameter and to correctly handle signal-dependent noise after PSF convolution, the work could advance self-supervised deblurring by providing a physics-informed mechanism for bias correction beyond zero-mean assumptions. The multi-frame initialization and pretrain-finetune components offer practical engineering value for stable training under realistic low-light conditions.

major comments (2)
  1. Abstract: The central claim that a frequency-domain constraint 'inherent to the defocus imaging process' can be enforced via a single learnable noise bias parameter for joint bias correction requires explicit derivation showing independence from the fitted term. The parameter is determined during training on target data, and low-light noise is typically signal-dependent (Poisson-Gaussian); without demonstrating that the constraint remains valid post-convolution with the defocus PSF, the physics guidance risks being circular.
  2. Abstract (and method description): The multi-frame initialization and pretrain-finetune steps are presented as suppressing biased noise prior to deblurring, but these do not remove the dependency on the learnable bias parameter for enforcing the constraint. Validation that the overall formulation is not merely empirical fitting is load-bearing for the 'physics-guided' claim.
minor comments (1)
  1. The abstract would benefit from a concise statement of the assumed noise model and the explicit form of the frequency-domain constraint to allow immediate assessment of its applicability to signal-dependent noise.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback, which highlights important aspects of our physics-guided formulation that require further clarification. We address the major comments point by point below and will revise the manuscript to incorporate explicit derivations and additional validation as requested.

read point-by-point responses

  1. Referee: Abstract: The central claim that a frequency-domain constraint 'inherent to the defocus imaging process' can be enforced via a single learnable noise bias parameter for joint bias correction requires explicit derivation showing independence from the fitted term. The parameter is determined during training on target data, and low-light noise is typically signal-dependent (Poisson-Gaussian); without demonstrating that the constraint remains valid post-convolution with the defocus PSF, the physics guidance risks being circular.

    Authors: We agree that an explicit derivation is essential to substantiate independence and address potential circularity. In the revised manuscript, we will add a dedicated subsection in the method section providing a step-by-step derivation from the defocus imaging model. This will show that the frequency-domain constraint (arising from the optical transfer function properties) is structurally independent of the additive bias term, which is isolated as a separate learnable parameter. For signal-dependent noise, we will include both theoretical analysis (extending the Poisson-Gaussian model through the linear PSF convolution) and controlled experiments demonstrating that the constraint remains valid post-convolution, with the bias parameter correcting the resulting offset without altering the underlying frequency relationship. These additions will strengthen the physics-guided claim. revision: yes

  2. Referee: Abstract (and method description): The multi-frame initialization and pretrain-finetune steps are presented as suppressing biased noise prior to deblurring, but these do not remove the dependency on the learnable bias parameter for enforcing the constraint. Validation that the overall formulation is not merely empirical fitting is load-bearing for the 'physics-guided' claim.

    Authors: We acknowledge that the initialization and pretrain-finetune strategies are complementary engineering components and do not replace the need for the constraint. To validate the physics-guided nature, the revised manuscript will include expanded ablation studies: (1) performance comparison with the frequency-domain constraint disabled (reducing to standard Noise2Noise), and (2) analysis of the learned bias parameter's consistency across noise levels and its correlation with the derived constraint rather than arbitrary fitting. These will be supported by quantitative metrics showing that enforcing the constraint yields improvements beyond what initialization alone achieves, confirming the formulation is not purely empirical. revision: yes

Circularity Check

1 steps flagged

Frequency-domain constraint enforced via learnable (fitted) noise bias parameter reduces to training fit by construction

specific steps
  1. fitted input called prediction [Abstract]
    "we derive a frequency-domain constraint inherent to the defocus imaging process and incorporate it into the learning framework via a learnable noise bias parameter"

    The constraint is presented as derived from physics, yet is incorporated and enforced solely through a learnable noise bias parameter whose value is determined during training on the target noisy multi-frame data. This reduces the 'derived constraint' to the fitted parameter by construction, so any performance gain from 'joint bias correction' is a statistical fit rather than an independent physical prediction.

full rationale

The paper claims to derive a frequency-domain constraint from the defocus imaging model and incorporate it via a learnable noise bias parameter. This makes the central 'physics-guided' element statistically forced by the fitted parameter on target data rather than an independent first-principles result. No other circular steps (self-citations or ansatzes) are evident from the provided text; the multi-frame initialization and pretrain-finetune are separate. The derivation chain is therefore partially circular at the constraint-enforcement step, consistent with a score of 6.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Based solely on abstract; the learnable noise bias parameter is a fitted free parameter, and the frequency-domain constraint is treated as a domain assumption from defocus physics with no independent verification shown.

free parameters (1)
  • learnable noise bias parameter
    Introduced to model and correct biased noise within the learning framework; its value is determined during training.
axioms (1)
  • domain assumption Frequency-domain constraint inherent to the defocus imaging process
    Derived from the physical model of defocus imaging and incorporated as the basis for the bias correction mechanism.

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