Abstract: To separate oscillating parts such as texture and noise from piecewise smooth parts,a new variational image decomposition model is presented.The second generation curvelets and local cosine bases are used to represent structure and texture respectively.The total variational sem-i 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 denoising algorithm is used to solve the new model. Experiments show that the approach is very robust to noise,and able to maintain edges and textures stably.