Variational Image Restoration and Decomposition in Shearlet Smoothness Spaces

We present the shearlet-based variational model for image restoration and decomposition. The new model can be seen as generalizations of DaubechiesTeschke's model. By using regularization term in shearlets smoothness spaces, and writing the problem in a shearlet framework, we obtain elegant shearlet shrinkage schemes. Furthermore, the model allows us to incorporate general bounded linear blur operators into the problem. The experiments on denoising, deblurring and decomposition of images show that our algorithm is very efficient.