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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 ISSN 1439-7358.
An open access version can be found in:
Official URL: http://dx.doi.org/10.1007/978-3-319-08025-3_2
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, Engineering and Medicine > 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: |
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| 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: |
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