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arxiv: 2604.20154 · v1 · submitted 2026-04-22 · 📡 eess.IV · cs.CV· cs.LG

Maximum Likelihood Reconstruction for Multi-Look Digital Holography with Markov-Modeled Speckle Correlation

Xi Chen , Arian Maleki , Shirin Jalali This is my paper

Pith reviewed 2026-05-09 23:29 UTC · model grok-4.3

classification 📡 eess.IV cs.CVcs.LG
keywords specklecorrelationinter-lookmulti-lookreconstructionunderlikelihoodacquisition
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The pith

A Markov-modeled maximum likelihood estimator for multi-look holographic reconstruction achieves near-ideal performance under strong inter-look speckle correlation by outperforming methods that assume independence.

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

Digital holography uses laser light to capture detailed images but suffers from speckle, a grainy noise pattern. Taking multiple measurements (looks) and averaging them reduces this noise when the looks are independent. In practice, equipment limits cause the noise patterns to be correlated, so simple averaging fails. The authors treat the correlation as a first-order Markov chain, where each look's speckle depends mainly on the previous one. They derive the statistical likelihood of the data under this model and solve a constrained maximum likelihood problem to recover the underlying clean reflectivity. The solver uses projected gradient descent, deep image priors for regularization, Monte Carlo sampling, and matrix-free operations to keep computation feasible. Simulations indicate the method stays effective even with strong correlation, nearly matching the performance of ideal independent looks while beating standard approaches that ignore the dependence.

Core claim

Simulation results demonstrate that the proposed approach remains robust under strong inter-look correlation, achieving performance close to the ideal independent-look scenario and consistently outperforming methods that ignore such dependencies.

Load-bearing premise

The inter-look speckle dependence can be accurately captured by a first-order Markov process, and the likelihood can be derived under a first-order Markov approximation without significant loss of fidelity.

Figures

Figures reproduced from arXiv: 2604.20154 by Arian Maleki, Shirin Jalali, Xi Chen.

Figure 1
Figure 1. Figure 1: Apertures in the imaging forward model ( [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Total CG iterations required at each PGD iteration for three different apertures. Monte [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The images reconstructed based on two different loss functions [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
read the original abstract

Multi-look acquisition is a widely used strategy for reducing speckle noise in coherent imaging systems such as digital holography. By acquiring multiple measurements, speckle can be suppressed through averaging or joint reconstruction, typically under the assumption that speckle realizations across looks are statistically independent. In practice, however, hardware constraints limit measurement diversity, leading to inter-look correlation that degrades the performance of conventional methods. In this work, we study the reconstruction of speckle-free reflectivity from complex-valued multi-look measurements in the presence of correlated speckle. We model the inter-look dependence using a first-order Markov process and derive the corresponding likelihood under a first-order Markov approximation, resulting in a constrained maximum likelihood estimation problem. To solve this problem, we develop an efficient projected gradient descent framework that combines gradient-based updates with implicit regularization via deep image priors, and leverages Monte Carlo approximation and matrix-free operators for scalable computation. Simulation results demonstrate that the proposed approach remains robust under strong inter-look correlation, achieving performance close to the ideal independent-look scenario and consistently outperforming methods that ignore such dependencies. These results highlight the importance of explicitly modeling inter-look correlation and provide a practical framework for multi-look holographic reconstruction under realistic acquisition conditions. Our code is available at: https://github.com/Computational-Imaging-RU/MLE-Holography-Markov.

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.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of modeling speckle correlation as a first-order Markov process and the accuracy of the resulting likelihood approximation; no free parameters or invented entities are explicitly introduced in the abstract.

axioms (1)
  • domain assumption Inter-look speckle realizations follow a first-order Markov process
    Invoked to derive the likelihood function from the multi-look measurements.

pith-pipeline@v0.9.0 · 5548 in / 1227 out tokens · 17411 ms · 2026-05-09T23:29:02.300919+00:00 · methodology

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Reference graph

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