Compressed Sensing Algorithm In Image Processing

In recent years, compressed sensing (CS) has attracted considerable attention in areas of applied mathematics, computer science, and electrical engineering by suggesting that it may be possible to surpass the traditional limits of sampling theory. CS builds upon the fundamental fact that we can represent many signals using only a few non-zero coeffcients in a suiTAB.le basis or dictionary. Nonlinear optimization can then enable recovery of such signals from very few measurements. In this paper, we provide an up-to-date review of the basic theory underlying CS.The main work and contribution are as follows:This study of article describes the theoretical framework of compressed sensing and sparse optimization and also discusses the problems in existing reconstruction algorithms. We verified a compressed sensing algorithm based on the the Bayesian CS of Laplace distribution to analysis of the algorithm and compared with the performance of the existing algorithms. This paper studies the compressed sensing theory reconstruction algorithm and the theory of compressed sensing application in image noise reduction and de-blur problem. Reconstruction algorithm as a key part in the theoretical core of compressed sensing which determines the reconstructed image quality and reconstruction speed. In this paper, we analysis the theories of existing algorithms and the use of compressed sensing theory in total variation model. Finally we use the total variation model in solving the Constrained TV-Based Image De-Noising and De-Blurring problems. Our algorithms produced an image whose PSNR was improved and stabilized. Compared with GP or other denoising and FTVd debluring methods, numerical examples illustrate its validity and advantage of reconstruction quality in our algorithms.