A Continuous-Domain Solution for Computed Tomography with Hessian Total-Variation Regularization
M. Pourya, Y. Haouchat, M. Unser
Proceedings of the Twenty-First IEEE International Symposium on Biomedical Imaging (ISBI'24), Aθήνα (Athens), Ελληνική Δημοκρατία (Hellenic Republic), May 27-30, 2024.
We formulate computed-tomography reconstruction as a continuous-domain optimization problem with Hessian total variation (HTV) as the regularizer. HTV is a sparsity-promoting regularizer that favors continuous and piecewise-linear functions with few affine pieces. We develop a computational scheme that yields a solution with arbitrary precision. We model the unknown signal using a box-spline basis. Our contributions involve exact formulas for the x-ray transform, HTV, and the refinement of the proposed model. We adopt a multiresolution optimization scheme that solves the continuous-domain problem. We validate our framework with numerical experiments.
@INPROCEEDINGS(http://bigwww.epfl.ch/publications/pourya2403.html,
AUTHOR="Pourya, M. and Haouchat, Y. and Unser, M.",
TITLE="A Continuous-Domain Solution for Computed Tomography with
{H}essian Total-Variation Regularization",
BOOKTITLE="Proceedings of the Twenty-First IEEE International Symposium
on Biomedical Imaging ({ISBI'24})",
YEAR="2024",
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month="May 27-30,",
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