Comparative study between different bases of transformation for compressive sensing of images

Compressive Sensing is a theory that can reconstruct a signal (or image) from a very small number of measurements, beyond the limits traditionally imposed by Shannon´s theorem. To make this reconstruction perfect, some conditions are necessary, the signal must be sparse in a known basis and the number of measures should be sufficient enough to be in accordance with the rate of the signal sparseness. In this paper, we propose to compare different bases of transformation for compressive sensing of images. For this purpose, we use the most popular transformations that are DWT, DCT, DT-CWT and Contourlet. For our study, we choose two of the most efficient image recovery methods. The first is the L₁-dantzig selector based on convex optimization approach, and the second is the Orthogonal Matching Pursuit (OMP) based on greedy algorithms. Experimental results show the efficiency of the DT-CWT in term of Peak Signal to Noise Ratio (PSNR) and Structural SIMilarity (SSIM) and also with the visual assessment of the reconstructed images.