Deep Regularized Compound Gaussian Network for Solving Linear Inverse Problems

• URL: http://arxiv.org/abs/2311.17248v3
• Date: Mon, 18 Mar 2024 15:35:52 GMT
• Title: Deep Regularized Compound Gaussian Network for Solving Linear Inverse Problems
• Authors: Carter Lyons, Raghu G. Raj, Margaret Cheney,
• Abstract summary: We devise two novel approaches for linear inverse problems that permit problem-specific statistical prior selections. The first method is an iterative algorithm that minimizes a regularized least squares objective function. The second method is a novel deep regularized (DR) neural network, called DR-CG-Net, that learns the prior information.
• Score: 1.283555556182245
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Incorporating prior information into inverse problems, e.g. via maximum-a-posteriori estimation, is an important technique for facilitating robust inverse problem solutions. In this paper, we devise two novel approaches for linear inverse problems that permit problem-specific statistical prior selections within the compound Gaussian (CG) class of distributions. The CG class subsumes many commonly used priors in signal and image reconstruction methods including those of sparsity-based approaches. The first method developed is an iterative algorithm, called generalized compound Gaussian least squares (G-CG-LS), that minimizes a regularized least squares objective function where the regularization enforces a CG prior. G-CG-LS is then unrolled, or unfolded, to furnish our second method, which is a novel deep regularized (DR) neural network, called DR-CG-Net, that learns the prior information. A detailed computational theory on convergence properties of G-CG-LS and thorough numerical experiments for DR-CG-Net are provided. Due to the comprehensive nature of the CG prior, these experiments show that DR-CG-Net outperforms competitive prior art methods in tomographic imaging and compressive sensing, especially in challenging low-training scenarios.

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