Nonlinear tomographic reconstruction via nonsmooth optimization
<|reference_start|>Nonlinear tomographic reconstruction via nonsmooth optimization: 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.<|reference_end|>
@article{charisopoulos2024nonlinear,
    title={Nonlinear tomographic reconstruction via nonsmooth optimization},
    author={Vasileios Charisopoulos, Rebecca Willett},
    journal={arXiv preprint arXiv:2407.12984},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.12984},
    primaryClass={math.OC cs.NA math.NA}
}