Cartoon + Texture Image Decomposition by the TV-L1 Model

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 L1 data fidelity term and a Total Variation (TV) regularization term. The L1 norm is particularly well suited for the cartoon+texture decomposition since it better preserves geometric features than the L2 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. Source Code The source code and the online demonstration are accessible at the IPOL web part of this article1.