Research On Signal Recovery Algorithms Based On Compressed Sensing

Compressed Sensing is a new signal processing theory. It takes full advantage of thesparsity or compressibility of the signal and can sample signal and compress data at thesame time. Firstly, it collects signals’s measured value that is far less than the length ofthe signal. And then reconstructs the signal by appropriate signal recovery algorithm.Compressed sensing break through the bottleneck of the Nyquist sampling theorem andis a new revolution in the field of signal processing. It has broad application prospects.Signal recovery algorithm is the core part of compressed sensing. This paperfocuses on the matching pursuit algorithm that is based on greedy iteration idea andproposes two new algorithms, which is based on the analysis and summary of theadvantages and disadvantages of various algorithms.Firstly, this paper introduces several classical matching pursuit algorithms in detail,and presents the principles and steps of the algorithms. At the same time, simulative testsare made to validate the algorithms. It not only analyzes and compares the performanceof the various algorithms, but also summarizes the advantages and disadvantages of thealgorithms.Secondly, the Sparsity Adaptive Matching Pursuit Algorithm (SAMP) is mainlydiscussed and researched in this paper. And on the basis of retaining SAMP’s sparsityadaptive idea, a new algorithm is proposed for the deficiencies in its atoms selectionmethod. The new algorithm guarantees that the residual which is generated in eachiteration is minimum, therefore the convergence speed of the algorithm is quickened andthe reconstruction accuracy is improved. The experimental results show that thealgorithm is superior to the original SAMP algorithm both in the reconstruction qualityand reconstruction speed, so it is a good greedy iterative algorithm.Finally, the Regurized Orthogonal Matching Pursuit Algorithm (ROMP) requires thesignal’s sparsity and lacks backtracking thought in the choice of atoms. In response to these, this paper proposes a new algorithm-Sparsity Adaptive-Backtracking-RegularizedOrthogonal Matching Pursuit Algorithm(SAB-ROMP).On the basis of the ROMPalgorithm, the new algorithm combines sparsity adaptive thought with backtrackingthought and overcomes the inherent disadvantages of the ROMP algorithm. Theexperimental results show that compared with the ROMP algorithm, the algorithm hashigher reconstruction accuracy when the sampling rate is high. And with the samplingrate increasing, this advantage is more prominent. However, the reconstruction time ofthe algorithm is much long, therefore, it is not suitable to use this method in large-scaleproblems.