Image compressed sensing based on DT-CWT

Compressed sensing (CS) aims to reconstruct signals and images from significantly fewer measurements than the traditional necessary. The step of reconstructing image is equivalent to find the sparse coefficients of image in a proper basis by solving a l₁ problem. This article implements the compressed sensing system using the sparse prior of image based on the 2D dual tree complex wavelet transform (2D DT-CWT) which has improved directional selectivity and approximate shift invariance. In this paper, we choose PDCT to get the measurements, and reconstruct the image from the measurements by iterative shrinkage. The experimental results demonstrate that one can get reconstructed image with higher quality based on DT-CWT combined with hard thresholding and total variation.