# Multilook Coherent Imaging: Theoretical Guarantees and Algorithms

arXiv: https://arxiv.org/abs/2505.23594 · HTML: https://mlsanity.com/paper/2505.23594/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 71 references that are in the map.
- First posted on arXiv 29 May 2025.

## Builds on (most cited first, 21 of 21)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networks](https://mlsanity.com/paper/1810.03982/) (2018)
- [DeepRED: Deep Image Prior Powered by RED](https://mlsanity.com/paper/1903.10176/) (2019)
- [Compressed Sensing with Deep Image Prior and Learned Regularization](https://mlsanity.com/paper/1806.06438/) (2018)
- [SUNet: Swin Transformer UNet for Image Denoising](https://mlsanity.com/paper/2202.14009/) (2022)
- [Denoising and Regularization via Exploiting the Structural Bias of Convolutional Generators](https://mlsanity.com/paper/1910.14634/) (2019)
- [Algorithmic Guarantees for Inverse Imaging with Untrained Network Priors](https://mlsanity.com/paper/1906.08763/) (2019)
- [Solving Inverse Problems with Hybrid Deep Image Priors: the challenge of preventing overfitting](https://mlsanity.com/paper/2011.01748/) (2020)
- [Provable Compressed Sensing with Generative Priors via Langevin Dynamics](https://mlsanity.com/paper/2102.12643/) (2021)
- [Blind Image Deblurring with Unknown Kernel Size and Substantial Noise](https://mlsanity.com/paper/2208.09483/) (2022)
- [Practical Phase Retrieval Using Double Deep Image Priors](https://mlsanity.com/paper/2211.00799/) (2022)
- [One-dimensional Deep Image Prior for Time Series Inverse Problems](https://mlsanity.com/paper/1904.08594/) (2019)
- [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)
- [Convergence Rate Improvement of Richardson and Newton-Schulz Iterations](https://mlsanity.com/paper/2008.11480/) (2020)
- [Is speckle noise more challenging to mitigate than additive noise?](https://mlsanity.com/paper/2409.16585/) (2024)

## Built on by (most cited first, 4 of 4)

- [Factor Informed Double Deep Learning For Average Treatment Effect Estimation](https://mlsanity.com/paper/2508.17136/) (2025)
- [Monte Carlo Maximum Likelihood Reconstruction for Digital Holography with Speckle](https://mlsanity.com/paper/2602.10344/) (2026)
- [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)

Multilook coherent imaging is a widely used technique in applications such as digital holography, ultrasound imaging, and synthetic aperture radar. A central challenge in these systems is the presence of multiplicative noise, commonly known as speckle, which degrades image quality. Despite the widespread use of coherent imaging systems, their theoretical foundations remain relatively underexplored. In this paper, we study both the theoretical and algorithmic aspects of likelihood-based approaches for multilook coherent imaging, providing a rigorous framework for analysis and method development. Our theoretical contributions include establishing the first theoretical upper bound on the Mean Squared Error (MSE) of the maximum likelihood estimator under the deep image prior hypothesis. Our results capture the dependence of MSE on the number of parameters in the deep image prior, the number of looks, the signal dimension, and the number of measurements per look. On the algorithmic side, we employ projected gradient descent (PGD) as an efficient method for computing the maximum likelihood solution. Furthermore, we introduce two key ideas to enhance the practical performance of PGD. First, we incorporate the Newton-Schulz algorithm to compute matrix inverses within the PGD iterations, significantly reducing computational complexity. Second, we develop a bagging strategy to mitigate projection errors introduced during PGD updates. We demonstrate that combining these techniques with PGD yields state-of-the-art performance. Our code is available at https://github.com/Computational-Imaging-RU/Bagged-DIP-Speckle.