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Reconciling Bayesian and perimeter regularization for binary inversion
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Dunbar, Oliver R. A., Dunlop, Matthew M., Elliott, Charles M., Hoang, Viet Ha and Stuart, Andrew M. (2020) Reconciling Bayesian and perimeter regularization for binary inversion. SIAM Journal on Scientific Computing, 42 (4). A1984-A2013. doi:10.1137/18M1179559
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WRAP-reconciling-Bayesian-perimeter-regularization-binary-inversion-Elliot-2020.pdf - Accepted Version - Requires a PDF viewer. Download (3147Kb) | Preview |
Official URL: https://doi.org/10.1137/18M1179559
Abstract
A central theme in classical algorithms for the reconstruction of discontinuous functions from observational data is perimeter regularization via the use of the total variation. On the other hand, sparse or noisy data often demands a probabilistic approach to the reconstruction of images, to enable uncertainty quantification; the Bayesian approach to inversion, which itself introduces a form of regularization, is a natural framework in which to carry this out. In this paper the link between Bayesian inversion methods and perimeter regularization is explored. In this paper two links are studied: (i) the maximum a posteriori (MAP) objective function of a suitably chosen Bayesian phase-field approach is shown to be closely related to a least squares plus perimeter regularization objective; (ii) sample paths of a suitably chosen Bayesian level set formulation are shown to possess finite perimeter and to have the ability to learn about the true perimeter.
| Item Type: | Journal Article | |||||||||||||||||||||||||||
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| Subjects: | Q Science > Q Science (General) Q Science > QA Mathematics Q Science > QC Physics |
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| Divisions: | Faculty of Science > Mathematics | |||||||||||||||||||||||||||
| Library of Congress Subject Headings (LCSH): | Bayesian statistical decision theory , Inverse problems (Differential equations), Level set methods , Convergence, Uncertainty (Information theory) | |||||||||||||||||||||||||||
| Journal or Publication Title: | SIAM Journal on Scientific Computing | |||||||||||||||||||||||||||
| Publisher: | Society for Industrial and Applied Mathematics | |||||||||||||||||||||||||||
| ISSN: | 1064-8275 | |||||||||||||||||||||||||||
| Official Date: | 2020 | |||||||||||||||||||||||||||
| Dates: |
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| Volume: | 42 | |||||||||||||||||||||||||||
| Number: | 4 | |||||||||||||||||||||||||||
| Page Range: | A1984-A2013 | |||||||||||||||||||||||||||
| DOI: | 10.1137/18M1179559 | |||||||||||||||||||||||||||
| Status: | Peer Reviewed | |||||||||||||||||||||||||||
| Publication Status: | Published | |||||||||||||||||||||||||||
| Publisher Statement: | First Published in SIAM Journal on Scientific Computing in 42(4), A1984–A2013. 2020, published by the Society for Industrial and Applied Mathematics (SIAM) Copyright © by SIAM. Unauthorized reproduction of this article is prohibited. | |||||||||||||||||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||||||||||||||
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