Multilook Coherent Imaging: Theoretical Guarantees and Algorithms

TL;DR

This paper provides the first theoretical bounds on the MSE of maximum likelihood estimators in multilook coherent imaging and introduces efficient algorithms, including PGD with Newton-Schulz and bagging, for improved image reconstruction.

Contribution

It establishes the first theoretical MSE bounds for likelihood-based multilook coherent imaging and develops enhanced PGD algorithms with practical improvements.

Findings

Theoretical MSE bounds depend on parameters like looks and measurements.

Proposed PGD with Newton-Schulz and bagging improves computational efficiency.

Achieves state-of-the-art performance in multilook coherent imaging.

Abstract

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.