A Compound Gaussian Least Squares Algorithm and Unrolled Network for Linear Inverse Problems
This work addresses image reconstruction challenges in fields like medical imaging and sensing, offering improved methods but is incremental as it builds on existing unrolled network and regularization techniques.
The paper tackles linear inverse problems in tomographic imaging and compressive sensing by developing a compound Gaussian least squares algorithm and an unrolled deep neural network, achieving state-of-the-art performance, particularly in low-training regimes.
For solving linear inverse problems, particularly of the type that appears in tomographic imaging and compressive sensing, this paper develops two new approaches. The first approach is an iterative algorithm that minimizes a regularized least squares objective function where the regularization is based on a compound Gaussian prior distribution. The compound Gaussian prior subsumes many of the commonly used priors in image reconstruction, including those of sparsity-based approaches. The developed iterative algorithm gives rise to the paper's second new approach, which is a deep neural network that corresponds to an "unrolling" or "unfolding" of the iterative algorithm. Unrolled deep neural networks have interpretable layers and outperform standard deep learning methods. This paper includes a detailed computational theory that provides insight into the construction and performance of both algorithms. The conclusion is that both algorithms outperform other state-of-the-art approaches to tomographic image formation and compressive sensing, especially in the difficult regime of low training.