Circular symmetric Shearlet transform and its application for image separation

In this paper, we firstly give a new discrete Shearlet transform by combining circular symmetric filter bank and shear operation. Then, we present a new combined dictionary consisting of wavelets and circular symmetric Shearlet and apply it to image separation based on geometric separation theory. Because of the combined dictionary sparsely represents point and curvilinear singularities respectively, the image can be decomposed into pointlike and curvelike parts as accurate as possible. We further give an efficient numerical scheme and discuss the advantage of this new algorithm.