Image Decomposition Model Using Curvelets and Wave Atoms

The aim of this paper is to combine curvelets with wave atoms by using the mixed constraints, namely smoothness of semi-norm of decomposition spaces and sparsity. It fully considers the sparse representation of curvelets and wave atoms. Curvelets are an essentially optimal representation of objects which is C² away from a C² edge, while wave atoms have a significantly sparser representation of the warped oscillatory functions or oriented textures than other fixed standard representations like wavelets, Gabor atoms, or curvelets. Moreover, the correlation of piecewise smooth component and textural component is employed as a stopping criterion to control the iterations. Experimental results and comparisons show the efficiency of the proposed models for image decomposition.