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Numerical analysis of the TV regularization and H-1 fidelity model for decomposing an image into cartoon plus texture
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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 ISSN 0272-4979.
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Official URL: http://dx.doi.org/10.1093/imanum/drn025
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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | IMA Journal of Numerical Analysis | ||||
Publisher: | Oxford University Press | ||||
ISSN: | 0272-4979 | ||||
Official Date: | July 2009 | ||||
Dates: |
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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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