Volume 54, pp. 108-127, 2021.

Analysis of the CCFD method for MC-based image denoising problems

Faisal Fairag, Ke Chen, and Shahbaz Ahmad


Image denoising using mean curvature leads to the problem of solving a nonlinear fourth-order integro-differential 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.

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Key words

image denoising, mean curvature, cell-centered finite difference method, numerical analysis

AMS subject classifications

68U10, 94A08, 65N06, 65N12

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