Skip to content Skip to navigation
University of Warwick
  • Study
  • |
  • Research
  • |
  • Business
  • |
  • Alumni
  • |
  • News
  • |
  • About

University of Warwick
Publications service & WRAP

Highlight your research

  • WRAP
    • Home
    • Search WRAP
    • Browse by Warwick Author
    • Browse WRAP by Year
    • Browse WRAP by Subject
    • Browse WRAP by Department
    • Browse WRAP by Funder
    • Browse Theses by Department
  • Publications Service
    • Home
    • Search Publications Service
    • Browse by Warwick Author
    • Browse Publications service by Year
    • Browse Publications service by Subject
    • Browse Publications service by Department
    • Browse Publications service by Funder
  • Help & Advice
University of Warwick

The Library

  • Login
  • Admin

A Bayesian level set method for geometric inverse problems

Tools
- Tools
+ Tools

Iglesias, Marco, Lu, Yulong and Stuart, A. M. (2016) A Bayesian level set method for geometric inverse problems. Interfaces and Free Boundaries, 18 (2). pp. 181-217. doi:10.4171/IFB/362 ISSN 1463-9963.

[img]
Preview
PDF
WRAP_1504.00313.pd.pdf - Accepted Version - Requires a PDF viewer.

Download (2917Kb) | Preview
Official URL: http://dx.doi.org/10.4171/IFB/362

Request Changes to record.

Abstract

We introduce a level set based approach to Bayesian geometric inverse problems. In these problems the interface between different domains is the key unknown, and is realized as the level set of a function. This function itself becomes the object of the inference. Whilst the level set methodology has been widely used for the solution of geometric inverse problems, the Bayesian formulation that we develop here contains two significant advances: firstly it leads to a well-posed inverse problem in which the posterior distribution is Lipschitz with respect to the observed data, and may be used to not only estimate interface locations, but quantify uncertainty in them; and secondly it leads to computationally expedient algorithms in which the level set itself is updated implicitly via the MCMC methodology applied to the level set function – no explicit velocity field is required for the level set interface. Applications are numerous and include medical imaging, modelling of subsurface formations and the inverse source problem; our theory is illustrated with computational results involving the last two applications.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Inverse problems (Differential equations), Bayesian statistical decision theory
Journal or Publication Title: Interfaces and Free Boundaries
Publisher: European Mathematical Society Publishing House
ISSN: 1463-9963
Official Date: 19 September 2016
Dates:
DateEvent
19 September 2016Published
28 February 2016Accepted
Volume: 18
Number: 2
Page Range: pp. 181-217
DOI: 10.4171/IFB/362
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 3 March 2017
Date of first compliant Open Access: 8 March 2017
Funder: Engineering and Physical Sciences Research Council (EPSRC), United States. Office of Naval Research
Grant number: EP/HO23364/1, Programme Grant EQUIP (EPSRC)

Request changes or add full text files to a record

Repository staff actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics

twitter

Email us: wrap@warwick.ac.uk
Contact Details
About Us