Variational image restoration and decomposition with curvelet shrinkage

The curvelet is more suitable for image processing than the wavelet and able to represent smooth and edge parts of image with sparsity. Based on this, we present a new model for image restoration and decomposition via curvelet shrinkage. The new model can be seen as a modification of Daubechies-Teschke's model. By replacing the B-p,q(beta) term by a G(p,q)(beta) term, and writing the problem in a curvelet framework, we obtain elegant curvelet shrinkage schemes. Furthermore, the model allows us to incorporate general bounded linear blur operators into the problem. Various numerical results on denoising, deblurring and decomposition of images are presented and they show that the model is valid.