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

arXiv: https://arxiv.org/abs/2604.20154 · HTML: https://mlsanity.com/paper/2604.20154/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 33 references that are in the map.
- First posted on arXiv 22 Apr 2026.

## Builds on (most cited first, 9 of 9)

- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Time-multiplexed Neural Holography: A flexible framework for holographic near-eye displays with fast heavily-quantized spatial light modulators](https://mlsanity.com/paper/2205.02367/) (2022)
- [Phase-error estimation and image reconstruction from digital-holography data using a Bayesian framework](https://mlsanity.com/paper/1708.01142/) (2017)
- [Depolarized Holography with Polarization-multiplexing Metasurface](https://mlsanity.com/paper/2309.14668/) (2023)
- [Bagged Deep Image Prior for Recovering Images in the Presence of Speckle Noise](https://mlsanity.com/paper/2402.15635/) (2024)
- [Stochastic Light Field Holography](https://mlsanity.com/paper/2307.06277/) (2023)
- [Monte Carlo Maximum Likelihood Reconstruction for Digital Holography with Speckle](https://mlsanity.com/paper/2602.10344/) (2026)

## Built on by (most cited first, 2 of 2)

- [Minimax Theory of Likelihood-Based Deep Learning for Speckle Regression](https://mlsanity.com/paper/2607.14064/) (2026)
- [Implicit Neural Speckle Denoising](https://mlsanity.com/paper/2608.06574/) (2026)

## Abstract (arXiv)

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.