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

arXiv: https://arxiv.org/abs/1912.01738 · HTML: https://mlsanity.com/paper/1912.01738/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Dec 2019.

## Built on by (most cited first, 1 of 1)

- [Benchmarking Diffusion Annealing-Based Bayesian Inverse Problem Solvers](https://mlsanity.com/paper/2503.03007/) (2025)

## Abstract (arXiv)

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.