Compressed Sensing by Wavelet-Based Contourlet Transform

Due to enormous information in images and people's increasing demand for it, high-speed sampling causes large date transmission and storage. In order to solve this problem, compressed sensing is proposed to directly acquire the important information about the images. As the use of an efficient representation implies the compactness of the compressed file, in this work, we apply a directional multiresolution analysis framework called wavelet-based contourlet as a sparse basis and a tight frame to compressed sensing. In our work, compared with the traditional basis, even though the power signal-to-noise ratio (PSNR) of recovery images by wavelet-based contourlet is lower than that by wavelet, intrinsic geometrical structures of these images are better preserved. In most circumstances, these preserved structures are quite significant for human visual system. Numerical experiments are presented to illustrate the superior performance of proposed method by dealing images which contain complex contours and textures.