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arxiv: 2606.25924 · v1 · pith:NU3MTPGGnew · submitted 2026-06-24 · 📡 eess.IV · physics.optics

Improving Richardson--Lucy Deconvolution with Diffusion Priors for Fluorescence Microscopy

Hao Chen , Scott S. Howard This is my paper

Pith reviewed 2026-06-25 19:42 UTC · model grok-4.3

classification 📡 eess.IV physics.optics
keywords Richardson-Lucy deconvolutiondiffusion priorsfluorescence microscopyPoisson noiseimage restorationgenerative modelslow-photon imaging
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The pith

A score-based diffusion prior inserted into Richardson-Lucy iterations reduces noise amplification while preserving weak filamentous and punctate structures in low-photon fluorescence microscopy.

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

The paper integrates a learned generative prior from score-based diffusion models into the Richardson-Lucy deconvolution process for fluorescence microscopy images. This occurs inside a decoupled inverse-problem framework where the diffusion prior supplies structural guidance across optimization iterations while the RL step continues to enforce consistency with measured photon counts under the Poisson imaging model. The goal is to mitigate the instability and noise amplification that arise when RL operates on measurements alone, which are insufficient to resolve fine biological detail. Unlike total-variation regularizers that often oversmooth, the diffusion prior is intended to guide recovery of weak structures without introducing the same degree of smoothing. Experiments across diverse samples and cellular morphologies report visibly reduced noise amplification and better retention of fine features at low photon counts.

Core claim

Integrating a score-based diffusion prior into the RL optimization iterations while retaining Poisson data consistency in the RL step produces deconvolved fluorescence images that exhibit reduced noise amplification and improved preservation of weak filamentous and punctate structures under low photon counts.

What carries the argument

A decoupled inverse-problem framework that alternates RL updates enforcing Poisson data fidelity with score-based diffusion prior steps that supply structural guidance.

If this is right

  • RL noise amplification decreases compared with unregularized or TV-regularized baselines.
  • Weak filamentous and punctate structures are recovered more faithfully than with total-variation regularization.
  • Convergence remains stable across low-photon regimes where standard RL becomes unstable.
  • The same framework applies to varied biological samples and cellular morphologies without retraining the RL step.

Where Pith is reading between the lines

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

  • The approach could be tested on simulated phantoms with known ground truth to quantify any residual bias introduced by the diffusion model.
  • If the diffusion prior is trained on a narrow class of structures, reconstructions of novel morphologies may systematically favor patterns seen during training.
  • The decoupled alternation suggests the method could be adapted to other Poisson-limited inverse problems in optical imaging by swapping the data-fidelity operator.
  • Performance gains might diminish if the diffusion model was not trained on data with matching noise statistics or resolution.

Load-bearing premise

The diffusion prior must supply structural guidance compatible with the Poisson imaging model when inserted into the RL iterations without introducing systematic bias or artifacts.

What would settle it

Reconstructed images that display artifacts or intensity distributions matching patterns from the diffusion model's training data rather than the true underlying fluorescence distribution would falsify the claim of unbiased guidance.

Figures

Figures reproduced from arXiv: 2606.25924 by Hao Chen, Scott S. Howard.

Figure 1
Figure 1. Figure 1: Overview of the Diffusion-RL framework. (A) Classical Richardson–Lucy (RL) deconvo￾lution iteratively restores an image using a known point-spread function (PSF). (B) The Diffusion-RL framework uses the diffusion model output as a warm initialization for RL, enabling repeated refine￾ment through iterative deconvolution updates. modified update: x (k+1) = x (k) ⊙ H∗  y α Hx(k) + ϵ  1 − λTV α ∇ ·  ∇x(k) √… view at source ↗
Figure 2
Figure 2. Figure 2: Unconditional diffusion sampling from the fluorescence prior. Synthetic patches are generated from pure Gaussian noise using the pretrained unconditional diffusion model. 2.5 Sampling and evaluation metrics At inference, the reverse trajectory is discretized into Nt = 100 total sampling steps using a standard Poly-7 noise schedule. At each step, the inner RL consistency loop runs for L = 6 iterations witho… view at source ↗
Figure 3
Figure 3. Figure 3: Comparisons on BPAE confocal fluorescence images. Confocal fluorescence microscopy reconstructions of BPAE cells are shown for (A) F-actin (Alexa Fluor 488 phalloidin), (B) mitochon￾dria (MitoTracker CMXRos, TxRed), and (C) nuclei (DAPI). For each target, the images compare the RAW measured input (α = 100), RL, TV-RL, Diffusion-RL, and the ground-truth (GT) reference. Insets for F-actin and mitochondria ar… view at source ↗
Figure 4
Figure 4. Figure 4: Reconstruction comparison under different photon-limited acquisition levels. Recon￾structions of widefield fluorescence images of HUVEC cells (ER/Nucleoli/RNA channel, 488 nm) under a 2D Gaussian PSF kernel are shown at (A) α = 5, (B) α = 10, (C) α = 100, and (D) α = 255. For each photon budget, the displayed images compare the RAW input, RL, TV-RL, Diffusion-RL, and the ground-truth (GT) reference. (E) PS… view at source ↗
Figure 5
Figure 5. Figure 5: Reconstruction comparison under different PSF kernels. Reconstructions of widefield fluorescence images of HUVEC cells in the Actin/RNA channel at 488 nm are shown at a fixed photon budget of α = 100 for three PSF settings: (A) Gaussian PSF with σ = 3 px and a 31×31 kernel; (B) Gaussian PSF with σ = 5 px and a 61×61 kernel; and (C) simulated PSF with 650 nm excitation and NA = 1.05. For each PSF kernel, th… view at source ↗
Figure 6
Figure 6. Figure 6: Diversity of Diffusion-RL reconstructions from stochastic sampling. Multiple Diffusion￾RL reconstructions are generated from different stochastic initializations for the same photon-limited measurement. The displayed examples include (A) BPAE mitochondria and (B) HEPG2 nuclei (widefield fluorescence, 378 nm). (C) Sample-to-sample variation under the same measurement condition, with PSNR and SSIM quantified… view at source ↗
read the original abstract

Richardson--Lucy (RL) deconvolution improves fluorescence microscopy images by recovering details lost to diffraction. It estimates the original fluorescence signal that most likely produced the measured photon counts under a Poisson imaging model. Although RL incorporates a physical model of fluorescence image formation and can improve contrast, deconvolution remains fundamentally ill-posed, and the measurements alone provide limited evidence for reliably reconstructing fine biological structure. Without additional structural guidance, RL can amplify noise and exhibit unstable convergence in low-photon regimes. Regularizers such as total variation (TV) reduce this instability but often introduce oversmoothing. Here, we investigate learned generative priors as a form of structural guidance for RL by integrating a score-based diffusion prior into a decoupled inverse-problem framework for fluorescence microscopy deconvolution. The diffusion prior is used during the RL optimization iterations, while RL retains Poisson data consistency. We validate the framework across diverse biological samples and cellular morphologies. The results show reduced RL noise amplification with improved preservation of weak filamentous and punctate structures under low photon counts.

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

3 major / 2 minor

Summary. The manuscript proposes integrating a score-based diffusion prior into a decoupled Richardson-Lucy (RL) deconvolution framework for fluorescence microscopy. RL retains the Poisson data-consistency term while the diffusion prior supplies structural guidance during iterations. The central claim is that this reduces noise amplification relative to standard RL and improves preservation of weak filamentous and punctate structures under low photon counts, with validation performed across diverse biological samples and cellular morphologies.

Significance. If the empirical improvements hold under quantitative scrutiny, the work would demonstrate a practical way to combine physical Poisson imaging models with learned generative priors without sacrificing data consistency, potentially outperforming hand-crafted regularizers such as total variation in low-light fluorescence imaging. The decoupled formulation and explicit retention of the RL Poisson term are positive design choices that avoid obvious circularity.

major comments (3)
  1. [Abstract] Abstract: the claim that results show 'reduced RL noise amplification with improved preservation of weak filamentous and punctate structures' is presented without any quantitative metrics (PSNR, SSIM, error bars, or statistical tests), making the central empirical claim impossible to verify from the supplied description.
  2. [Method] Method description: the precise mechanism by which the diffusion prior is inserted into the RL iterations (the 'decoupled inverse-problem framework') is not specified with update equations or pseudocode; without this, it is impossible to confirm that the prior supplies guidance compatible with the Poisson model without introducing systematic bias or artifacts, which is load-bearing for the weakest assumption identified in the reader's note.
  3. [Validation/Results] Validation section: the statement that the framework was 'validated across diverse biological samples' supplies no details on the number of samples, photon-count regimes tested, or comparison baselines (standard RL, TV-RL), so the reported improvements cannot be assessed for reproducibility or generality.
minor comments (2)
  1. Add a table or figure panel with quantitative metrics and error analysis to support the qualitative claims in the abstract.
  2. Clarify notation for the diffusion score and how it is scaled or projected within each RL iteration.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback. We address each major comment below and will revise the manuscript accordingly to improve clarity and verifiability.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that results show 'reduced RL noise amplification with improved preservation of weak filamentous and punctate structures' is presented without any quantitative metrics (PSNR, SSIM, error bars, or statistical tests), making the central empirical claim impossible to verify from the supplied description.

    Authors: We agree that the abstract would benefit from quantitative support. In the revised manuscript we will add specific PSNR/SSIM values, error bars, and statistical test results to substantiate the claims about noise reduction and structure preservation. revision: yes

  2. Referee: [Method] Method description: the precise mechanism by which the diffusion prior is inserted into the RL iterations (the 'decoupled inverse-problem framework') is not specified with update equations or pseudocode; without this, it is impossible to confirm that the prior supplies guidance compatible with the Poisson model without introducing systematic bias or artifacts, which is load-bearing for the weakest assumption identified in the reader's note.

    Authors: The current manuscript indeed omits the explicit update equations and pseudocode for the decoupled framework. We will include the full mathematical formulation and algorithmic steps in the revision to demonstrate how the diffusion prior is integrated while preserving Poisson data consistency. revision: yes

  3. Referee: [Validation/Results] Validation section: the statement that the framework was 'validated across diverse biological samples' supplies no details on the number of samples, photon-count regimes tested, or comparison baselines (standard RL, TV-RL), so the reported improvements cannot be assessed for reproducibility or generality.

    Authors: We acknowledge the lack of detail on sample counts, photon regimes, and baselines. The revised results section will specify the number of samples, tested photon counts, and direct quantitative comparisons against standard RL and TV-RL to enable assessment of reproducibility and generality. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The abstract and described approach combine the established Richardson-Lucy Poisson deconvolution with an external score-based diffusion prior inserted for guidance only, while explicitly retaining the RL data-consistency term. No equations, self-citations, or claims reduce any reported improvement (e.g., reduced noise amplification or better preservation of filamentous structures) to a fitted parameter, renamed input, or self-referential definition. The framework is presented as a modular integration of two independent components, with validation across samples rather than any internal reduction to the inputs. This matches the default expectation of a non-circular paper.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim depends on the diffusion prior being able to guide reconstruction without violating the Poisson consistency term; no free parameters or invented entities are mentioned in the abstract.

axioms (1)
  • domain assumption The diffusion prior can be inserted into RL iterations while retaining Poisson data consistency.
    Explicitly stated as the core of the proposed framework in the abstract.

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discussion (0)

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