Image Decomposition Based on Curvelet and Wave Atom

To separate oscillating parts such as texture and noise from piecewise smooth parts, a new variational image decomposition model is presented, which well improve the novel Starck's model. The second generation curvelets and wave atoms are used to represent structure and texture respectively. The total variation semi-norm is added for restricting structure parts. The generalized homogeneous Besov norm proposed by Meyer is used to constrain noisy components. Finally, the Basis Pursuit Denoisiing algorithm is used to solve the new model. Experiments show that the approach is very robust to noise, and that can keep edges and textures stably.