Combined Curvelet Shrinkage and Nonlinear Anisotropic Diffusion

Combined Curvelet Shrinkage and Nonlinear Anisotropic Diffusion Jianwei Ma 1 and Gerlind Plonka 2 1 Laboratoire LMC-IMAG, University Joseph Fourier, BP 53, 38041 Grenoble Cedex 9, France [email protected] 2 Department of Mathematics, University of Duisburg-Essen, Campus Duisburg, 47048 Duisburg, Germany [email protected] Abstract In this paper, a diffusion-based curvelet shrinkage is proposed for discontinuity-preserving denoising using a combination of a new tight frame of curvelets with a nonlinear diffusion scheme. In order to suppress the pseudo-Gibbs and curvelet-like artifacts, the conventional shrinkage results are further processed by a projected total variation diffusion, in which only the in- significant curvelet coefficients or high-frequency part of the signal are changed by use of a constrained projection. Numerical experiments from piecewise-smooth to textured images show good performances of the proposed method to recover the shape of edges and important detailed components, in comparison to some existing methods. Mathematics Subject Classification 2000. 65T60, 65M06, 65M12, 94A12. Key words. Curvelets, nonlinear diffusion, regularization, discontinuity-preserving, denoising. 1

Combined Curvelet Shrinkage and Nonlinear Anisotropic Diffusion

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curvelets

nonlinear diffusion

regularization

discontinuitypreserving

denoising