Research On Recovery Algorithms In Compressive Sensing

Compressed Sensing (CS) theory is a novel mechanism for signal processing, whichcontains three core issues: sparsify process of signal, construction of measurementmatrix and design of recovery algorithm.Firstly, this paper introduces three common sparsify processes of signal viatheoretical basis and simulation experiment in detail; then according to the condition ofrestricted isometry property (RIP) and coherence, the paper introduces some randommatrices satisfying RIP in sense of probability and four kinds of deterministic matricessatisfying low coherence; Lastly, the paper lists three recovery algorithms, whoseperformance are compared via a large number of simulation experiments. As for twounstable algorithms: Orthogonal Matching Pursuit (OMP) and Iterative HardThresholding (IHT) algorithm, this paper further research the algorithms with betterperformance.As for the unstable performance of OMP algorithm in recovering0-1signals, thispaper firstly theoretically analyzes the performance of original algorithm in recoveringmagnitude decaying signal; and then proposes the Sensing Dictionary-based OrthogonalMatching Pursuit (SDOMP) algorithm on the basis of sensing dictionary theory. Thisalgorithm can improve recovery performance via pairs of sensing dictionary andmeasurement matrix with low coherence from Sensing Dictionary algorithm. Besides,the sufficient condition under which SDOMP can exactly recover original sparse signalis proposed based on Restricted Cross Isometry Property (RCIP), and the effectivenessof the SDOMP algorithm is verified through simulation experiments. The algorithm hasthree important properties:1) measurement matrix and recovery algorithm areconstructed collaboratively;2) the constructed measurement matrix can be used asdeterministic one;3) the new designed algorithm can maintain the low computationalcomplexity of original algorithm.This paper designs the Orthogonal Iterative Hard Thresholding (OIHT) algorithmby putting orthogonal projection (or pseudo inverse) into iteration process of IterativeHard Thresholding (IHT) algorithm. The convergence speed, computational complexityand recovery performance are shown through theoretical analysis and simulationexperiment. And then the paper proposes a Stepwise Suboptimal Iterative HardThresholding (SSIHT) algorithm, whose performance are indicated via the simulation ofrecovering Gaussian sparse signals and0-1signals.