# Monte Carlo Maximum Likelihood Reconstruction for Digital Holography with Speckle

arXiv: https://arxiv.org/abs/2602.10344 · HTML: https://mlsanity.com/paper/2602.10344/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 39 references that are in the map.
- First posted on arXiv 10 Feb 2026.

## Builds on (most cited first, 11 of 11)

- [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)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networks](https://mlsanity.com/paper/1810.03982/) (2018)
- [Plug-and-Play Unplugged: Optimization Free Reconstruction using Consensus Equilibrium](https://mlsanity.com/paper/1705.08983/) (2017)
- [Learning a Dilated Residual Network for SAR Image Despeckling](https://mlsanity.com/paper/1709.02898/) (2017)
- [Phase-error estimation and image reconstruction from digital-holography data using a Bayesian framework](https://mlsanity.com/paper/1708.01142/) (2017)
- [Bagged Deep Image Prior for Recovering Images in the Presence of Speckle Noise](https://mlsanity.com/paper/2402.15635/) (2024)
- [Multilook Coherent Imaging: Theoretical Guarantees and Algorithms](https://mlsanity.com/paper/2505.23594/) (2025)
- [DoPAMINE: Double-sided Masked CNN for Pixel Adaptive Multiplicative Noise Despeckling](https://mlsanity.com/paper/1902.02530/) (2019)
- [CLAMP: Majorized Plug-and-Play for Coherent 3D LIDAR Imaging](https://mlsanity.com/paper/2406.13651/) (2024)

## Built on by (most cited first, 1 of 1)

- [Maximum Likelihood Reconstruction for Multi-Look Digital Holography with Markov-Modeled Speckle Correlation](https://mlsanity.com/paper/2604.20154/) (2026)

## Abstract (arXiv)

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.