Elliott, Charles M. and Smitheman, S. A. (2009) Numerical analysis of the TV regularization and H-1 fidelity model for decomposing an image into cartoon plus texture. IMA Journal of Numerical Analysis, Vol.29 (No.3). pp. 651-689. doi:10.1093/imanum/drn025

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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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Journal or Publication Title:	IMA Journal of Numerical Analysis
Publisher:	Oxford University Press
ISSN:	0272-4979
Official Date:	July 2009
Dates:	Date Event July 2009 Published
Volume:	Vol.29
Number:	No.3
Page Range:	pp. 651-689
DOI:	10.1093/imanum/drn025
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

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