Research On Signal Reconstruction Algorithms For Compressed Sensing

Compressed Sensing(CS) theory breaks the limitations of the traditional Nyquist samplingtheorem, and it provides a method to recover the original signal from a small amount of samples.For sparse and compressible signal, compressed sensing makes the signal compression during thesampling. It’s a good solution to the contradiction between the traditional sampling theory andreality signal processing. CS demonstrates outstanding advantages and a broad applicationprospects in the field of modern signal processing. This thesis introduces the CS theory in detail andmakes a in-depth research for measurement matrix and signal reconstruction algorithm for CS. Themain work is as follows:(1)An improved Hadamard measurement matrix based on Hadamard matrix is proposed in thisthesis. The new measurement matrix is constructed from low dimensional to high dimensional withlinear expression of orthogonal basises, and the basises is generated from Hadamard matrix. Thelinear coefficients of basises are combined with deterministic numbers and Gauss numbers.Simulation results show that the new measurement matrix has a better performance.(2)The greedy algorithms used in CS are introduced in this thesis. Firstly, we brieflysummarize the classification of greedy algorithms. Then, we make a in-depth analysis ofOrthogonal Matching Pursuit, Subspace Pursuit and Sparsity Adaptive Matching Pursuit bysimulating.(3)This thesis introduces a two-stage sparsity adaptive greedy algorithm: forward-backwardpursuit algorithm(FBP). And we give a new variable step size forward-backward pursuit algorithmbased on FBP, which is called VsFBP. VsFBP adjusts the iteration step size adaptively which canreduce the running time during improving the algorithm’s performance. The simulation resultsdemonstrate the better performance of the VsFBP algorithm.