The Research On Reconstruction Algorithms Based On The Compressed Sensing Theory

Compressed Sensing (CS) theory receives widespread concern immediately when it is proposed. The CS breaks the traditional way of signal processing, and combines the signal sampling and compression together. It brings a big change to signal processing. The precondition of the CS theory is the sparsity of the signal. Currently there are three important research directions in CS theory:sparse signal representation, research of the measurement matrix and the design of the reconstruction algorithm. The reconstruction algorithm is the most important of the three aspects for it is the last step to application. So the research of the CS theory has important implications.In this paper, the CS process is introduced from the basic CS theory. Study and summarize the existing common reconstruction algorithm deeply, especially for the orthogonal matching pursuit, generalized orthogonal matching pursuit and subspace pursuit. Through these three algorithms, two improved ways are proposed.The main contents of this paper and the results obtained are as follows:(1)Introduce the three most important of the CS theory:sparse signal representation, research of the measurement matrix and the design of the reconstruction algorithm. Summarize the existing common reconstruction algorithm. Compare the efficiency, the frequency of the reconstruction and the reconstruction quality through the simulation experiments. Research is focused on the class of the matching pursuit algorithm, especially the orthogonal matching pursuit, generalized orthogonal matching pursuit and subspace pursuit.(2)The orthogonal matching pursuit algorithm has low reconstruction quality and the initial support set constituted by the initial K atoms has important influence on the reconstruction quality. Combined these two propertied, an algorithm called orthogonal matching-subspace pursuit is proposed. This algorithm use the K atoms selected by OMP algorithm as the initial support set to improve the quality of the original algorithms. Simulation results show that, regardless of the one-dimensional signal or two-dimensional image signal, the reconstruction quality has significantly improved compared to the original two algorithms.(3)The Generalized Orthogonal Matching Pursuit algorithm improves the efficiency of the Orthogonal Matching Pursuit algorithm greatly, but the selection of the step size is a big problem. If the step size is too large, it will lead a sharp decline in frequency of exact reconstruction and quality of the reconstruction. And if the step size is too small, the efficiency will not be improved. The optimal value of the step size is decided by the signal itself, which is difficult to know before the reconstruction. Adaptive thinking is used in this paper. Small step is used at first in the beginning iteration. The step size will be increased if the residuals decrease slowly in the next iterations. The simulation results show that this algorithm proposed in the paper can select a near-optimal step size, and has good reconstruction efficiency and quality.