Texture Separation BV-G and BV-L1 Models

In this work, we compare two models that were proposed to improve the well-known model of Rudin, Osher, and Fatemi [Phys. D, 60 (1992), pp. 259–268]. The first one, proposed by Meyer [Oscillating Patterns in Image Processing and in Some Nonlinear Evolution Equations. The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures, Univ. Lecture Ser. 22, AMS, Providence, RI, 2001], is the BV −G model, and the second one is the BV −L1 model. We state the similitudes between both models. In particular, we prove a characterization theorem for optimal decompositions for the BV − L1 model. We then compare these models in the particular case of radial functions.