Nonlinear tomographic reconstruction via nonsmooth optimization
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910532204756992 |
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| author | Charisopoulos, Vasileios Willett, Rebecca |
| author_facet | Charisopoulos, Vasileios Willett, Rebecca |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_12984 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonlinear tomographic reconstruction via nonsmooth optimization Charisopoulos, Vasileios Willett, Rebecca Optimization and Control Numerical Analysis 65K10, 90C06 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. |
| title | Nonlinear tomographic reconstruction via nonsmooth optimization |
| topic | Optimization and Control Numerical Analysis 65K10, 90C06 |
| url | https://arxiv.org/abs/2407.12984 |