Image decomposition combining a total variational filter and a Tikhonov quadratic filter

Abstract

In this paper, we propose a new variational model for image decomposition which separates an image into a cartoon, consisting only of geometric objects and an oscillatory component, consisting of texture or noise. In the new model, the $$\hbox {H}^{-1}$$H-1-norm is considered as the data fitting term and the regularization term is composed of a total variational filter and a Tikhonov quadratic filter. These two filters can be automatically selected by a soft threshold function. When the pixels belong to the cartoon area, the total variational filter is adopted, which can preserve the geometric structures of image such as the edges, well. When the pixels belong to texture region, the Tikhonov quadratic filter is chosen,which can extract the texture of image well. To solve the proposed model effectively, the split Bregman method is employed. Experimental results demonstrate that the proposed model and algorithm can obtain better decomposition results than those of classical models.