Abstract
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.
Abstract (translated)
为了解决线性逆问题，特别是出现在磁共振成像和压缩感知中的问题，本文开发了两种新的算法。第一种方法是迭代算法，其最小化的目标是 regularized 最小二乘法 objective function，其中Regularization是基于组合高斯先验分布的。组合高斯先验分布将许多在图像重建中常用的先验包括在内，包括基于密度的先验。开发迭代算法导致本文提出的第二种新算法，这是一种深度神经网络，与迭代算法的“展开”或“展开”对应。展开的深度神经网络具有可解释的层，并比标准深度学习方法表现更好。本文包括详细的计算理论，提供了对两个算法构造和性能的理解。结论是，两个算法在磁共振成像和压缩感知中的表现优于其他先进的方法，特别是在低训练状态下。
URL
https://arxiv.org/abs/2305.11120
