ANALYSIS OF THE CCFD METHOD FOR MC-BASED IMAGE DENOISING PROBLEMS

Fairag, Faisal, Chen, Ke ORCID: 0000-0002-6093-6623 and Ahmad, Shahbaz (2021) ANALYSIS OF THE CCFD METHOD FOR MC-BASED IMAGE DENOISING PROBLEMS. ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS, 54. pp. 108-127.

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Official URL: http://dx.doi.org/10.1553/etna_vol54s108

Abstract

Image denoising using mean curvature leads to the problem of solving a nonlinear fourth-order integrodifferential equation. The nonlinear fourth-order term comes from the mean curvature regularization functional. In this paper, we treat this high-order nonlinearity by reducing the nonlinear fourth-order integro-differential equation to a system of first-order equations. Then a cell-centered finite difference scheme is applied to this system. With a lexicographical ordering of the unknowns, the discretization of the mean curvature functional leads to a block pentadiagonal matrix. Our contributions are fourfold: (i) we give a new method for treating the high-order nonlinearity term; (ii) we express the discretization of this term in terms of simple matrices; (iii) we give an analysis for this new method and establish that the error is of first order; and (iv) we verify this theoretical result by illustrating the convergence rates in numerical experiments.

Item Type:	Article
Uncontrolled Keywords:	image denoising, mean curvature, cell-centered finite difference method, numerical analysis
Depositing User:	Symplectic Admin
Date Deposited:	11 Jan 2021 09:56
Last Modified:	18 Jan 2023 23:04
DOI:	10.1553/etna_vol54s108
Open Access URL:	http://etna.mcs.kent.edu/vol.54.2021/pp108-127.dir...
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3113036