An Edge-preserving Variational Method for Image Decomposition

Variational methods for image decomposition have gained considerable attention in recent years. In such approaches, an image usually can be decomposed into a geometrical (or structure) component and a textured (or noise) feature. In this paper we propose an edge-preserving variational model which can split an image into four components: a first one containing the structure of the image, a second one the texture of the image, a third one the noise and a forth one the edge. Our decomposition model relies on the use of three different terms: the edge-preserving regularization for the geometrical component and the edge, a negative Sobolev norm for the texture, and a negative Besov norm for the noise. We explicitly give numerical scheme that is the synthesis of a projection algorithm, a redundant wavelet (or curvelet) soft threshold and two coupled Partial differential equations (PDE's). Finally we show image decomposition results on synthetic and real image.