Provably Convergent Learned Inexact Descent Algorithm for Low-Dose CT Reconstruction

We propose an Efficient Inexact Learned Descent-type Algorithm (ELDA) for a class of nonconvex and nonsmooth variational models, where the regularization consists of a sparsity enhancing term and non-local smoothing term for learned features. The ELDA improves the performance of the LDA in Chen et al. (SIAM J Imag Sci 14(4), 1532–1564, 2021) by reducing the number of the subproblems from two to one for most of the iterations and allowing inexact gradient computation. We generate a deep neural network, whose architecture follows the algorithm exactly for low-dose CT (LDCT) reconstruction. The network inherits the convergence behavior of the algorithm and is interpretable as a solution of the varational model and parameter efficient. The experimental results from the ablation study and comparisons with several state-of-the-art deep learning approaches indicate the promising performance of the proposed method in solution accuracy and parameter efficiency.