Consistent Discretizations for Vanishing Regularization Solutions to Image Processing Problems

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

[img] 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 View Item