# Nonlinear tomographic reconstruction via nonsmooth optimization

arXiv: https://arxiv.org/abs/2407.12984 · HTML: https://mlsanity.com/paper/2407.12984/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jul 2024.

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

- [Accurate, provable and fast polychromatic tomographic reconstruction: A variational inequality approach](https://mlsanity.com/paper/2503.19925/) (2025)

## Abstract (arXiv)

We study iterative signal reconstruction in computed tomography (CT), wherein measurements are produced by a linear transformation of the unknown signal followed by an exponential nonlinear map. Approaches based on pre-processing the data with a log transform and then solving the resulting linear inverse problem are tempting since they are amenable to convex optimization methods; however, such methods perform poorly when the underlying image has high dynamic range, as in X-ray imaging of tissue with embedded metal. We show that a suitably initialized subgradient method applied to a natural nonsmooth, nonconvex loss function produces iterates that converge to the unknown signal of interest at a geometric rate under the statistical model proposed by Fridovich-Keil et al. (arXiv:2310.03956). Our recovery program enjoys improved conditioning compared to the formulation proposed by the latter work, enabling faster iterative reconstruction from substantially fewer samples.