The Research Of Image Reconstruct Algorithm Based On Compressed Sensing

For many years, the theoretical basis to guide the sampling signal has always been the well-known Nyquist sampling theorem. The theorem requires that the signal sampling rate should not be less than twice the maximum frequency of the signal, which brings high requirements to the system processing ability and significant challenges to the corresponding internal and external hardware. Compressed sensing (CS) theory gives a new approach to reconstruct original signals from a few observation values, with the priori knowledge that the signal has the sparse representation.This paper first describes the basic framework of the compressed sensing theory, along with a thorough study on spare decomposition, observation matrix and signal reconstruction of the two-dimensional image. On this basis, this paper studies several compressed sensing algorithms, and proposes two effective compression sensing reconstruction algorithm upon its shortcomings.To solve the problems of excessive smoothness, long reconstruction time and etc. of in the compressed sensing block iterative projection algorithm, overlapping observation matrix design is introduced and adaptive projection iterative method and compressed sensing reconstruction algorithm based on landweber iteration fast projection is proposed. Moreover, the impact of overlapping step size parameters on algorithm is discussed comprehensively the experiment. The experimental results show that the algorithm has a good performance in reconstruction quality and running time.In the consideration of the problem that effective reconstruction only works when more observation values is provided to orthogonal matching pursuit algorithm, this paper introduces an observation matrix design method based on the image information to adaptively ensure observation number. Meanwhile, in order to make the algorithm more sparse representative, using K-SVD dictionary training method to get sparse dictionary, this paper proposes adaptive observation number orthogonal matching pursuit algorithm based on the redundant dictionary. Experimental results verify that the algorithm not only solves the problem that the observation number is low, but also offers good image reconstruction quality.