Cartoon + Texture Image Decomposition by the TV-L1 Model

Abstract

We consider the problem of decomposing an image into a cartoon part and a textural part. The geometric and smoothly-varying component, referred to as cartoon, is composed of object hues and boundaries. The texture is an oscillatory component capturing details and noise. Variational models form a general framework to obtain u + v image decompositions, where cartoon and texture are forced into different functional spaces. The TV-L1 model consists in a L 1 data fidelity term and a Total Variation (TV) regularization term. The L 1 norm is particularly well suited for the cartoon+texture decomposition since it better preserves geometric features than the L 2 norm. The TV regularization has become famous in inverse problems because it enables to recover sharp variations. However, the nondifferentiability of TV makes the underlying problems challenging to solve. There exists a wide literature of variants and numerical attempts to solve these optimization problems. In this paper, we present an implementation of a primal dual algorithm proposed by Antonin Chambolle and Thomas Pock applied to this image decomposition problem with the TV-L1 model. A thorough experimental comparison is performed with a recent filter pair proposed in IPOL for the cartoon+texture decomposition.