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

2026-04-21

AI Summary

This work addresses the challenge in multi-view digital holographic imaging where hardware constraints induce spatially correlated speckle noise across views, violating the conventional assumption of statistical independence and degrading denoising and reconstruction performance. The authors propose the first method to explicitly model inter-view speckle correlations as a first-order Markov process, formulating a constrained maximum likelihood estimation framework. By integrating deep image priors as implicit regularization and leveraging matrix-free operators with projected gradient descent for efficient optimization, the approach achieves high-fidelity reconstructions even under strong speckle correlation—conditions where traditional methods fail. Experimental results demonstrate that the proposed technique significantly outperforms existing approaches and nearly attains the reconstruction quality achievable under idealized independent-view assumptions.

Technology Category

• Machine Learning: Multi-instance/Multi-view Learning
• Computer Vision: Multi-modal Vision
• Intelligent Robots: State Estimation

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Security and Privacy: Data transparency and provenance
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• multi-look digital holography
• speckle correlation
• coherent imaging
• inter-look dependence
• reflectivity reconstruction

Innovation

• Markov-modeled speckle correlation
• maximum likelihood reconstruction
• multi-look digital holography
• deep image priors
• projected gradient descent