LAMA-Net: A Convergent Network Architecture for Dual-Domain Reconstruction

Abstract

We propose a learnable variational model that learns the features and leverages complementary information from both image and measurement domains for image reconstruction. In particular, we introduce a learned alternating minimization algorithm (LAMA) from our prior work, which tackles two-block nonconvex and nonsmooth optimization problems by incorporating a residual learning architecture in a proximal alternating framework. In this work, our goal is to provide a complete and rigorous convergence proof of LAMA and show that all accumulation points of a specified subsequence of LAMA must be Clarke stationary points of the problem. LAMA directly yields a highly interpretable neural network architecture called LAMA-Net. Notably, in addition to the results shown in our prior work, we demonstrate that the convergence property of LAMA yields outstanding stability and robustness of LAMA-Net in this work. We also show that the performance of LAMA-Net can be further improved by integrating a properly designed network that generates suitable initials, which we call iLAMA-Net. To evaluate LAMA-Net/iLAMA-Net, we conduct several experiments and compare them with several state-of-the-art methods on popular benchmark datasets for Sparse-View Computed Tomography.