Total Variation Based Image Cartoon-Texture Decomposition‡

This paper studies algorithms for decomposing a real image into the sum of cartoon and texture based on total variation minimization and secondorder cone programming (SOCP). The cartoon is represented as a function of bounded variation while texture (and noise) is represented by elements in the space of oscillating functions, as proposed by Yves Meyer. Our approach gives more accurate results than those obtained previously by Vese-Osher’s approximation to Meyer’s model, which we also formulate and solve as an SOCP. The model of minimizing total variation with an L1-norm fidelity term is also considered and empirically shown to achieve even better results when there is no noise. This model is analyzed and shown to be able to select features of an image according to their scales.