Compressed Sensing Image Reconstruction Based on Sparse Image Representation Using Dual-tree Complex wavelet and Wave atoms

At present most algorithms applied to compressed sensing image reconstruction are based on the prior of images have sparse representation in single basis. However, many images have sparse representation in more than one basis, when the image is represented by one basis, it can’t capture the image structure effectively, and results in the bad quality of recovered image. In this paper, we propose a compressed sensing system based on the image have sparse representation on wave atoms and the dual tree complex wavelet transform (DTCWT), making use of the linear Bregman iteration to reconstruct the original image. The algorithm regulate the total variation with the gradient descend method after updating in each iteration, and then performs the soft-thresholding on these two bases respectively to reduce the l1 norm of the image. The results of experiments show that our algorithm effectively improves the quality of the recovered image.