Skip Navigation


IMA Journal of Numerical Analysis Advance Access originally published online on June 25, 2008
IMA Journal of Numerical Analysis 2009 29(3):651-689; doi:10.1093/imanum/drn025
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
29/3/651    most recent
drn025v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Elliott, C. M.
Right arrow Articles by Smitheman, S. A.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Numerical analysis of the TV regularization and H–1 fidelity model for decomposing an image into cartoon plus texture

C. M. Elliott{dagger} and S. A. Smitheman

Department of Mathematics, University of Sussex, Brighton BN1 9RF, UK

{dagger} Email: c.m.elliott{at}warwick.ac.uk

Received on 12 October 2006. Revised on 27 June 2007.


  Abstract

The Osher–Solé–Vese (OSV) model, which is the gradient flow of an energy consisting of the total variation functional plus an H–1 fidelity term, is studied. In this paper, we build on the analysis of the OSV model which we gave in Elliott & Smitheman (2007, Comm. Pure Appl. Anal., in press). We introduce backward Euler finite-element approximations to a regularized version of the OSV initial boundary-value problem (IBVP) and to a weak formulation of the original problem. Well-posedness and unconditional Lyapunov stability of these fully discrete schemes are proved. Convergence results as the spatial mesh parameter, the time step size and the regularization parameter tend to 0 are proved. Rates of convergence as the time step size and the regularization parameter tend to 0 are found. The existence, uniqueness and Lyapunov stability of a solution to a linearly implicit finite-element approximation to the regularized version of the OSV IBVP are also proved.

Key Words: image decomposition; cartoon plus texture; TV and H–1 model; fourth-order parabolic equation; numerical analysis


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.