Monte Carlo Maximum Likelihood Reconstruction for Digital Holography with Speckle

2026-02-10

AI Summary

This work addresses the challenge of multiplicative speckle noise in coherent imaging, which severely limits high-resolution reconstruction in digital holography. Conventional maximum likelihood approaches are often impractical due to the prohibitive computational cost of high-dimensional matrix inversion. To overcome this, the authors propose the PGD-MC framework, which, for the first time, enables physically accurate aperture modeling within a maximum likelihood reconstruction without relying on simplifying assumptions. The method efficiently computes the likelihood gradient via conjugate gradient iterations—avoiding explicit matrix inversion—and integrates projected gradient descent with Monte Carlo estimation, augmented by plug-and-play regularization that fuses three denoisers. This approach achieves high reconstruction accuracy while significantly improving computational efficiency, enabling high-resolution applications. Experimental results demonstrate its superiority over existing model-based iterative methods in both reconstruction quality and speed, confirming its effectiveness, flexibility, and scalability in speckle suppression.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Matrix & Tensor Methods
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

In coherent imaging, speckle is statistically modeled as multiplicative noise, posing a fundamental challenge for image reconstruction. While maximum likelihood estimation (MLE) provides a principled framework for speckle mitigation, its application to coherent imaging system such as digital holography with finite apertures is hindered by the prohibitive cost of high-dimensional matrix inversion, especially at high resolutions. This computational burden has prevented the use of MLE-based reconstruction with physically accurate aperture modeling. In this work, we propose a randomized linear algebra approach that enables scalable MLE optimization without explicit matrix inversions in gradient computation. By exploiting the structural properties of sensing matrix and using conjugate gradient for likelihood gradient evaluation, the proposed algorithm supports accurate aperture modeling without the simplifying assumptions commonly imposed for tractability. We term the resulting method projected gradient descent with Monte Carlo estimation (PGD-MC). The proposed PGD-MC framework (i) demonstrates robustness to diverse and physically accurate aperture models, (ii) achieves substantial improvements in reconstruction quality and computational efficiency, and (iii) scales effectively to high-resolution digital holography. Extensive experiments incorporating three representative denoisers as regularization show that PGD-MC provides a flexible and effective MLE-based reconstruction framework for digital holography with finite apertures, consistently outperforming prior Plug-and-Play model-based iterative reconstruction methods in both accuracy and speed. Our code is available at: https://github.com/Computational-Imaging-RU/MC_Maximum_Likelihood_Digital_Holography_Speckle.

Problem

• speckle
• maximum likelihood estimation
• digital holography
• coherent imaging
• aperture modeling

Innovation

• Monte Carlo estimation
• maximum likelihood reconstruction
• digital holography
• speckle mitigation
• randomized linear algebra