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Title: Reconciling Bayesian and perimeter regularization for binary inversion
Authors: Dunbar, Oliver R. A.
Dunlop, Matthew M.
Elliott, Charles M.
Hoang, Viet Ha
Stuart, Andrew M.
Keywords: Engineering::Mathematics and analysis
Issue Date: 2020
Source: Dunbar, O. R. A., Dunlop, M. M., Elliott, C. M., Hoang, V. H. & Stuart, A. M. (2020). Reconciling Bayesian and perimeter regularization for binary inversion. SIAM Journal On Scientific Computing, 42(4), A1984-A2013.
Project: RG30/16
AGS 1835860
Journal: SIAM Journal on Scientific Computing
Abstract: A central theme in classical algorithms for the reconstruction of discontinuous functions from observational data is perimeter regularization via the use of total variation. On the other hand, sparse or noisy data often demand 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 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 a finite perimeter and to have the ability to learn about the true perimeter.
ISSN: 1064-8275
DOI: 10.1137/18M1179559
Schools: School of Physical and Mathematical Sciences 
Rights: © 2020 Society for Industrial and Applied Mathematics. All rights reserved. This paper was published in SIAM Journal on Scientific Computing and is made available with permission of Society for Industrial and Applied Mathematics.
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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