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Phase field methods for binary recovery

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Brett, Charles E. A., Elliott, Charles M. and Dedner, Andreas (2014) Phase field methods for binary recovery. Optimization with PDE Constraints, 101 . pp. 25-63. doi:10.1007/978-3-319-08025-3_2

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Official URL: http://dx.doi.org/10.1007/978-3-319-08025-3_2

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Abstract

We consider the inverse problem of recovering a binary function from blurred and noisy data. Such problems arise in many applications, for example image processing and optimal control of PDEs. Our formulation is based on the Mumford-Shah model, but with a phase field approximation to the perimeter regularisation. We use a double obstacle potential as well as a smooth double well potential. We introduce an iterative method for solving the problem, develop a suitable discretisation of this iterative method, and prove some convergence results. Numerical simulations are presented which illustrate the usefulness of the approach and the relative merits of the phase field models.

Item Type: Journal Article
Divisions: Faculty of Science > Mathematics
Series Name: Lecture Notes in Computational Science and Engineering
Journal or Publication Title: Optimization with PDE Constraints
Publisher: Springer, Cham
ISBN: 9783319080246
ISSN: 1439-7358
Book Title: Optimization with PDE Constraints
Editor: Hoppe, R.
Official Date: 2014
Dates:
DateEvent
2014Published
Volume: 101
Page Range: pp. 25-63
DOI: 10.1007/978-3-319-08025-3_2
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Open Access Version:
  • ArXiv

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