Abstract:

This paper presents a new method for image separation through employing a combined dictionary consisting of wavelets and complex shearlets. Because the combined dictionary sparsely represents points and curvilinear singularities respectively, the image can be decomposed into pointlike and curvelike parts as accurate as possible. The proposed method based on the geometric separation theory introduced by Donoho in 2005 shows that accurate geometric separation of the morphologically distinct features of points and curves can be achieved by l1 minimization. The experimental results show that the proposed method can not only be effective but also greatly reduce the computing time.