Proximal Newton Methods for X-Ray Imaging with Non-Smooth Regularization

TL;DR

This paper explores the application of proximal Newton methods to solve non-smooth regularized image reconstruction problems, specifically in X-ray CT, demonstrating potential advantages over first-order methods like FISTA.

Contribution

It introduces the use of proximal Newton algorithms for nonlinear X-ray CT reconstruction with TV regularization and compares their performance to existing first-order methods.

Findings

Proximal Newton methods can be more efficient than FISTA in certain scenarios.

Performance depends on regularization strength and Hessian approximation.

Exact Hessian use influences convergence speed.

Abstract

Non-smooth regularization is widely used in image reconstruction to eliminate the noise while preserving subtle image structures. In this work, we investigate the use of proximal Newton (PN) method to solve an optimization problem with a smooth data-fidelity term and total variation (TV) regularization arising from image reconstruction applications. Specifically, we consider a nonlinear Poisson-modeled single-energy X-ray computed tomography reconstruction problem with the data-fidelity term given by the I-divergence. The PN algorithm is compared to state-of-the-art first-order proximal algorithms, such as the well-established fast iterative shrinkage and thresholding algorithm (FISTA), both in terms of the number of iterations and time to solutions. We discuss the key factors that influence the performance of PN, including the strength of regularization, the stopping criterion for both sub-problem and main-problem, and the use of exact or approximated Hessian operators.