For solving linear inverse problems, particularly of the type that appear in
tomographic imaging and compressive sensing, this paper develops two new
approaches. The first approach is an iterative algorithm that minimizers 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.

本文为解决线性反演问题，并提出了两种新的算法：一种是基于复合高斯先验分布的正则最小平方目标函数迭代算法，另一种是对迭代算法的展开得到的深度神经网络。两种算法在断层成像和压缩感知等方面表现优异。