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Reconciling Bayesian and Total Variation Methods for Binary Inversion

Dunlop, Matthew M. and Elliott, Charles M. and Hoang, Viet Ha and Stuart, Andrew M. (2017) Reconciling Bayesian and Total Variation Methods for Binary Inversion. . (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20190404-111026312

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Abstract

A central theme in classical algorithms for the reconstruction of discontinuous functions from observational data is perimeter regularization. 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 is a natural framework in which to carry this out. The link between Bayesian inversion methods and perimeter regularization, however, is not fully understood. In this paper two links are studied: (i) the MAP objective function of a suitably chosen phase-field Bayesian 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. Furthermore, the level set approach is shown to lead to faster algorithms for uncertainty quantification than the phase field approach.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1706.01960arXivDiscussion Paper
ORCID:
AuthorORCID
Dunlop, Matthew M.0000-0001-7718-3755
Additional Information:The research of CME was partially supported by the Royal Society via a Wolfson Research Merit Award; the work of AMS by DARPA contract contract W911NF-15-2-0121; the work of CME and AMS by the EPSRC programme grant EQUIP; the work of MMD and AMS by AFOSR Grant FA9550-17-1-0185 and ONR Grant N00014-17-1-2079; the work of MMD by the EPSRC MASDOC Graduate Training Program; VHH gratefully acknowledges the MOE AcRF Tier 1 grant RG30/16.
Funders:
Funding AgencyGrant Number
Royal SocietyUNSPECIFIED
Army Research Office (ARO)W911NF-15-2-0121
Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
Engineering and Physical Sciences Research Council (EPSRC)EQUIP
Air Force Office of Scientific Research (AFOSR)FA9550-17-1-0185
Office of Naval Research (ONR)N00014-17-1-2079
Ministry of Education (Singapore)RG30/16
Subject Keywords:Bayesian inversion, phase-field, level set method, perimeter regularization, Gamma convergence, uncertainty quantification
Classification Code:AMS subject classifications. 35J35, 62G08, 62M40, 94A08
Record Number:CaltechAUTHORS:20190404-111026312
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20190404-111026312
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:94458
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:04 Apr 2019 19:44
Last Modified:04 Apr 2019 19:44

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