A Deep Compound Gaussian Regularized Unfolded Imaging Network

To solve linear inverse problems in image estimation, this paper develops an iterative algorithm that solves an implicitly regularized least squares problem where the chosen regularization is formulated on a compound Gaussian prior. The compound Gaussian prior, which decomposes the sparse coefficients of an image into a scale vector and Gaussian vector, subsumes many of the commonly used priors, including those of sparsity-based approaches. An implicit regularization on the scale vector permits application-specific variations for the iterative algorithm by specifying a regularization, or scale vector density, that fits the problem at hand. This iterative algorithm is then recast into a deep neural network through the algorithm unrolling, or unfolding, technique. The resultant unfolded deep neural network learns the implicit regularization from application-specific data, which, in effect, learns a generalization of the compound Gaussian prior that best applies to the given data. The algorithm unfolding approach, in general, produces high-performance deep neural networks that have interpretable layers. Through experimental testing, we conclude that our unfolded deep neural network outperforms other state-of-the-art iterative approaches to tomographic image formation.