Reconciling Bayesian and Perimeter Regularization for Binary Inversion
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.
Additional Information
© 2020 Society for Industrial and Applied Mathematics. Submitted to the journal's Methods and Algorithms for Scientific Computing section April 9, 2018; accepted for publication (in revised form) April 9, 2020; published electronically July 6, 2020. 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. The work of the first, third, and fifth authors was supported by the EPSRC programme grant EQUIP.Attached Files
Published - 18m1179559.pdf
Submitted - 1706.01960.pdf
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Additional details
- Alternative title
- Bayesian Formulations of Multidimensional Barcode Inversion
- Eprint ID
- 78108
- Resolver ID
- CaltechAUTHORS:20170612-125032088
- NSF
- AGS-1835860
- Royal Society
- Ministry of Education (Singapore)
- RG30/16
- Defense Advanced Research Projects Agency (DARPA)
- W911NF-15-2-0121
- Engineering and Physical Sciences Research Council (EPSRC)
- EQUIP
- Created
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2017-06-12Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field