Nonlinear tomographic reconstruction via nonsmooth optimization

Vasileios Charisopoulos; Rebecca Willett

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arXiv · 2407.12984

Nonlinear tomographic reconstruction via nonsmooth optimization

Vasileios Charisopoulos·Rebecca Willett

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Abstract

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.

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Vasileios Charisopoulos, Rebecca Willett. 2024-07-17. Nonlinear tomographic reconstruction via nonsmooth optimization. https://arxiv.org/abs/2407.12984

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