Multilook Coherent Imaging: Theoretical Guarantees and Algorithms

2025-05-29

AI Summary

Multiplicative speckle noise severely degrades image quality in multi-look coherent imaging modalities—including digital holography, ultrasound, and synthetic aperture radar (SAR)—posing a fundamental challenge for quantitative analysis and interpretation. To address this, this paper establishes a likelihood-based theoretical and algorithmic framework for speckle suppression. First, it derives, for the first time under the deep image prior (DIP) paradigm, the mean-squared error (MSE) lower bound for maximum likelihood estimation (MLE) in multiplicative noise models. Second, it introduces two key algorithmic innovations: (i) Newton–Schulz accelerated matrix inversion for efficient computation of the Fisher information matrix, and (ii) a bagging-based projection correction strategy to enhance the robustness and convergence stability of projected gradient descent (PGD). Extensive experiments demonstrate state-of-the-art performance in multi-look speckle reduction across diverse modalities. Both the theoretical bound and algorithmic efficacy are empirically validated via publicly available open-source implementations.

Technology Category

• Machine Learning: Multi-instance/Multi-view Learning
• Reasoning under Uncertainty: Stochastic Optimization
• Computer Vision: Multi-modal Vision

Application Category

• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• Addressing multiplicative noise in multilook coherent imaging
• Establishing theoretical bounds for maximum likelihood estimator MSE
• Enhancing projected gradient descent with efficient algorithms

Innovation

• Establishes theoretical MSE bounds for imaging
• Uses projected gradient descent for solutions
• Incorporates Newton-Schulz for matrix inverses