Reconciling Bayesian and perimeter regularization for binary inversion

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 uncer...

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Main Authors: Dunbar, Oliver R. A., Dunlop, Matthew M., Elliott, Charles M., Hoang, Viet Ha, Stuart, Andrew M.
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2021
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Online Access:https://hdl.handle.net/10356/147617
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1476172023-02-28T19:53:36Z Reconciling Bayesian and perimeter regularization for binary inversion Dunbar, Oliver R. A. Dunlop, Matthew M. Elliott, Charles M. Hoang, Viet Ha Stuart, Andrew M. School of Physical and Mathematical Sciences Engineering::Mathematics and analysis Bayesian Inversion Phase Field 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. Ministry of Education (MOE) Published version The work of the first author was supported by the NSF through grant AGS 1835860. The work of the third author was partially supported by the Royal Society via a Wolfson Research Merit Award. The work of the fourth author was supported by MOE AcRF Tier 1 grant RG30/16. The work of the fifth author was supported by DARPA through contract W911NF-15-2-0121. Thework of the first, third, and fifth authors was supported by the EPSRC programme grant EQUIP. The work of the first, second, third, and fifth authors was supported by the EPSRC. 2021-04-13T08:02:30Z 2021-04-13T08:02:30Z 2020 Journal Article 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. https://dx.doi.org/10.1137/18M1179559 1064-8275 https://hdl.handle.net/10356/147617 10.1137/18M1179559 2-s2.0-85093532255 4 42 A1984 A2013 en RG30/16 AGS 1835860 SIAM Journal on Scientific Computing © 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. application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Engineering::Mathematics and analysis
Bayesian Inversion
Phase Field
spellingShingle Engineering::Mathematics and analysis
Bayesian Inversion
Phase Field
Dunbar, Oliver R. A.
Dunlop, Matthew M.
Elliott, Charles M.
Hoang, Viet Ha
Stuart, Andrew M.
Reconciling Bayesian and perimeter regularization for binary inversion
description 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.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Dunbar, Oliver R. A.
Dunlop, Matthew M.
Elliott, Charles M.
Hoang, Viet Ha
Stuart, Andrew M.
format Article
author Dunbar, Oliver R. A.
Dunlop, Matthew M.
Elliott, Charles M.
Hoang, Viet Ha
Stuart, Andrew M.
author_sort Dunbar, Oliver R. A.
title Reconciling Bayesian and perimeter regularization for binary inversion
title_short Reconciling Bayesian and perimeter regularization for binary inversion
title_full Reconciling Bayesian and perimeter regularization for binary inversion
title_fullStr Reconciling Bayesian and perimeter regularization for binary inversion
title_full_unstemmed Reconciling Bayesian and perimeter regularization for binary inversion
title_sort reconciling bayesian and perimeter regularization for binary inversion
publishDate 2021
url https://hdl.handle.net/10356/147617
_version_ 1759858085239717888