Variational Image Decomposition in Shearlet Smoothness Spaces

Shearlet representation has gained more prominence in recent year as a flexible mathematical framework which enables the efficient analysis of anisotropic phenomena by combining multiscale analysis with the ability to handle directional information. Based on this, we present a new variational model for image decomposition in shearlet smoothness spaces. The new model can be seen as generalizations of Daubechies -Teschke´s model. By replacing the Besov regularization term by a shearlet-based regularization term, and writing the problem in a shearlet framework, we obtain elegant shearlet shrinkage schemes. The experiments on decomposition of images show that our algorithm is very efficient.