Katsaounis, Theodoros and Keeling, Stephen and Plexousakis, Michael
(2013)
*Consistent Discretizations for Vanishing Regularization Solutions to Image Processing Problems.*
(Submitted)

Text
acmac-0227.pdf Download (527Kb) |

## Abstract

A model problem is used to represent a typical image processing problem of reconstructing an unknown in the face of incomplete data. A consistent discretization for a vanishing regularization solution is defined so that, in the absence of noise, limits first with respect to regularization and then with respect to grid refinement agree with a continuum counterpart defined in terms of a saddle point formulation. It is proved and demonstrated computationally for an artificial example and for a realistic example with magnetic resonance images that a mixed finite element discretization is consistent in the sense defined here. On the other hand, it is demonstrated computationally that a standard finite element discretization is not consistent, and the reason for the inconsistency is suggested in terms of theoretical and computational evidence.

Item Type: | Article |
---|---|

Subjects: | Q Science > QA Mathematics |

Depositing User: | prof Theodoros Katsaounis |

Date Deposited: | 30 Apr 2013 05:06 |

Last Modified: | 18 Aug 2017 10:27 |

URI: | http://preprints.acmac.uoc.gr/id/eprint/227 |

### Actions (login required)

View Item |