Superiorization-inspired unrolled SART algorithm with U-Net generated perturbations for sparse-view and limited-angle CT reconstruction.

Unrolled algorithms are a promising approach for reconstruction of CT images in challenging scenarios, such as low-dose, sparse-view and limited-angle imaging. In an unrolled algorithm, a fixed number of iterations of a reconstruction method are unrolled into multiple layers of a neural network, and interspersed with trainable layers. The entire network is then trained end-to-end in a supervised fashion, to learn an appropriate regularizer from training data. In this paper we propose a novel unrolled algorithm, and compare its performance with several other approaches on sparse-view and limited-angle CT.The proposed algorithm is inspired by the superiorization methodology, an optimization heuristic in which iterates of a feasibility-seeking method are perturbed between iterations, typically using descent directions of a model-based penalty function. Our algorithm instead uses a modified U-net architecture to introduce the perturbations, allowing a network to learn beneficial perturbations to the image at various stages of the reconstruction, based on the training data.In several numerical experiments modeling sparse-view and limited angle CT scenarios, the algorithm provides excellent results. In particular, it outperforms several competing unrolled methods in limited-angle scenarios, while providing comparable or better performance on sparse-view scenarios.This work represents a first step towards exploiting the power of deep learning within the superiorization methodology. Additionally, it studies the effect of network architecture on the performance of unrolled methods, as well as the effectiveness of the unrolled approach on both limited-angle CT, where previous studies have primarily focused on the sparse-view and low-dose cases.