Signal Recovery Technique And Its Implementation Based On Compressed Sensing

Compressed sensing theory is a new kind of signal processing theory. It takes thesignal sparse as the the prerequisite, and breaks through the limitations of the traditionalsignal acquisition theory, which complete the signal sampling and compression in onestep to avoid the resource waste as the traditional sampling compression. Moreover,compressed sensing theory can use a small amount of samples values to recover theoriginal signal accurately, and it is widely applied in many fields.Firstly, This article briefly introduces the basic principle, mathematical model ofcompressed sensing theory and the three key technologies; secondly, the existingrecovery algorithms are studied in detail, which include greedy algorithms (MP、OMP、ROMP、SP、CoSaMP、SAMP) and convex optimization algorithms (BP、GPSR、TV).Simulation results and detailed analysis have been carried out, then compare theperformance of the algorithms. Since the existing recovery algorithms under lowsampling rate can not accurately recovery the original signal, we propose a recoveryalgorithm based on the convex optimization to solve the problems, and then discuss theidea and the process of the two representative algorithms (IRL1, IRLS) in detail.Compared with the greedy algorithm and convex optimization, the nonconvex recoveryalgorithm has obvious advantages in sparse signal recovery; finally, In order to facilitatethe follow-up study, in this paper we design the related graphical user interface, andrealize all the proposed algorithm.