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Bayesian Formulations of Multidimensional Barcode Inversion

Dunlop, Matthew M. and Elliott, Charles M. and Hoang, Viet Ha and Stuart, Andrew M. (2017) Bayesian Formulations of Multidimensional Barcode Inversion. . (Submitted) https://resolver.caltech.edu/CaltechAUTHORS:20170612-125032088

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Abstract

A pair of Bayesian approaches to the reconstruction of binary functions in R^d, d=2,3, is adopted; one is based on a Ginzburg-Landau penalized Gaussian prior, the other on a Bayesian level set formulation. For the Ginzburg-Landau approach a link is made to classical methods based on least squares constrained to piecewise constant functions, with a total variation regularization term which penalizes interfaces. This link rests on a careful choice, and scaling with respect to noise amplitude, of the prior and of the Ginzburg-Landau penalty. The key technical tool used to establish links between the Bayesian and classical approaches is the use of Γ− limits to study the MAP estimator. Furthermore, the parameter choices and scalings are shown, by means of numerical experiments, to lead to posterior concentration around a point which adequately encapsulates the truth. However, the Bayesian level set method is also shown to produce reconstructions of similar quality, at considerably lower computational cost, suggesting that the Bayesian level set method may be a viable alternative to total variation regularization for certain problems. The numerical studies are conducted using function-space MCMC.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
https://arxiv.org/abs/1706.01960arXivDiscussion Paper
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 and the work of CME and AMS by the EPSRC programme grant EQUIP. MMD was partially supported by the EPSRC MASDOC Graduate Training Program. VHH gratefully acknowledges the MOE AcRF Tier 1 grant RG30/16.
Funders:
Funding AgencyGrant Number
Royal SocietyUNSPECIFIED
Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
Engineering and Physical Sciences Research Council (EPSRC)UNSPECIFIED
Ministry of Education (Singapore)RG30/16
Subject Keywords:Ginzburg-Landau, Gamma-convergence, level set method, Bayesian inverse problems, imaging, binary reconstruction
Record Number:CaltechAUTHORS:20170612-125032088
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170612-125032088
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78108
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:12 Jun 2017 20:57
Last Modified:03 Oct 2019 18:05

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