Image reconstruction for compressed sensing based on the combined sparse image representation

For a natural image which includes both edge and texture information, the single basis function cannot reconstruct the image for compressed sensing optimally. In this paper, according to the Meyer's cartoon-texture model and biological vision function, the smooth and edge components are represented by Laplacian pyramid and circular symmetric contourlet, respectively, and the narrow-band contourlet is constructed to represent texture component sparsely. The basis functions of the three sparse transforms are similar to the receptive fields of the lateral geniculate nucleus, simple cells and grating cells in primary visual cortex. On the basis of the three sparse image representations and convex alternative projection algorithm, the image reconstruction for compressed sensing based on the combined sparse representation is proposed. Compared to the image reconstruction algorithm of block matching 3D transform shrinkage, the proposed algorithm can achieve higher image reconstruction performance. © 2010 Acta Automatica Sinica.