Compressive sensing with modified Total Variation minimization algorithm

In this paper, the reconstruction problem of compressive sensing algorithm that is exploited for image compression, is investigated. Considering the Total Variation (TV) minimization algorithm, and by adding some new constraints compatible with typical image properties, the performance of the reconstruction is improved. Using DCT and contourlet transforms, sparse expansion of the image are exploited to provide new constraints to remove irrelevant vectors from the feasible set of the optimization problem while keeping the problem as a standard Second Order Cone Programming (SOCP) one. Experimental results show that, the proposed method, with new constraints, outperforms the conventional TV minimization method by up to 2 dB in PSNR.