Compressed Sensing Based on the Contourlet Transform for Image Processing

In the compressed sensing, the sparse image is the prior condition. Contourlet transform is a non-adaptive multi-directional and multi-scale geometric analysis method, which could represent the image with contour and texture-rich more effective and has strong capability of nonlinear approximation. In this chapter, based on the advantages of Contourlet transform and the theory compressed sensing, an improved compressed sensing algorithm based on Contourlet transform was proposed. The improved compressed sensing algorithm only measured the high-pass Contourlet coefficients of the image but preserving the low-pass Contourlet coefficients. Then the image could be reconstructed by the inverse Contourlet transform. Compared with the traditional wavelet transformation in the compressed sensing image application, simulation results demonstrated that the proposed algorithm improved the quality of the recovered image significantly. For the same measurement number, the PSNR of the proposed algorithm was improved about 1.27–2.84 dB.