The Image Collecting And Reconstruction Algorithm Based On Compressed Sensing

As a new information acquisition and processing of theoretical framework, compressed sensing(CS) breaks the traditional Nyquist-shannon sampling theory, and has became a hot issue in signal processing fields. Under the condition that the signal is sparse and the measurement is incoherence, it uses frequency sampling rate which is far below the Nyquist-shannon frequency sampling rate to collect signal, and can accurately recover the original signal by some reconstruction algorithms.On the basis of domestic and foreign research, this dissertation firstly analyzes the basic theory of CS, then studies the image collecting and reconstruction algorithms which based on CS. To construct suitable deterministic measurement matrix and improve the accuracy of image reconstruction algorithm, the research mainly focuses on the common measurement matrices and the greedy pursuit algorithm. The contributions of this dissertation are summarized as follows:First, two kinds of measurement matrix based on low density parity check code(LDPC) are proposed. In review of the present commonly used random measurement matrices, computation is complex, large storage space are required and it is not easy to implemented on hardware. Considering that the decoding of LDPC codes is very similar to the reconstruction of CS, proposed the Gallager echelon structure parity check matrix used as a measurement matrix applied on compressed sensing. Meanwhile, combined the PEG algorithm and quasi cyclic extension method, a new algorithm is presented for constructing measurement matrix. Theoretical analysis shows that the two new measurement matrix is superior to the existed common measurement matrix in correlation and the non-diagonal maximum value of Gram matrix, and needs less storage space also easier to be implemented on hardware.Second, focusing on the error introduced by a support-set expansion with a fixed K-maximum of the inner product in each iteration of SP algorithm, a new adaptive look-ahead subspace pursuit algorithm is developed by employing a look-ahead strategy and a method to adaptively choose the best number of step. The results show that this algorithm not only improves the accuracy of signal reconstruction, but also balances the time required to the reconstruction.The experiments are carried on Matlab, and simulation results show that in many cases the proposed measurement matrices perform better than other commonly used measurement matrices, and the new reconstruction algorithm also performs better than other greedy pursuit algorithms in the reconstruction of one dimensional signal and two dimensional image.