Research Of Compressed Sensing Reconstruction Algorithms Based On Matrix Decomposition

Traditional signal processing technology follows the law of Nyquist sampling signals, that the sampling frequency must be greater than two times of the highest frequency that the signal can be accurately restore. Therefore, the traditional signal processing technology have been formed by contradiction in growing demand of signal. In recent years, a new signal processing technology was proposed by some related scholars, which is the Compressed Sensing technology. The technology demonstrated a huge advantage when it was compared with the traditional signal processing technology, which combined collection and compression of signal. It had broken the shackles of the law of Nyquist and the signal can be restored accurately. When the theory of compressed Sensing technology was put forwarded, compressed sensing theory has been received widespread attention by people, and has become a hot topic in the field of signal processing research. The theory has great application prospects, which has important significance both in filed of research theory and practical application.This thesis firstly introduces the background and the research significance of compressed sensing theory, and the research status at home and abroad is introduced simply. Then this thesis introduces the overall framework of compressed sensing theory, and expounds the three steps of the process of perception:sparse representation of signal, the design of the observation matrix and the signal reconstruction algorithm. In the part of sparse representation of signal, this thesis introduces the basic principle of signal sparse; To the design of the observation matrix, the selecting principle of the observation matrix is firstly analyzed, then several observation matrix are given. This thesis mainly studies the signal reconstruction algorithm, aiming at several main signal reconstruction algorithm, that the orthogonal matching pursuit algorithm and its improved algorithm are mainly introduced. Several algorithms for the MATLAB simulation are compared and analyzed. Based on the classical orthogonal matching pursuit algorithm, which the least squares method was used in part of signal reconstruction, but the complexity is higher in the process of matrix calculation with least squares calculation, and least squares is applied to each iteration. In the light of this, the principle of least square method is introduced, and several common methods of the matrix decomposition are listed, such as the QR decomposition, the cholesky decomposition and singular value decomposition are suitably applied to least squares. On this basis, the matrix QR decomposition is used in the orthogonal matching pursuit algorithm, and deduces the simplified results. Simulate the improved algorithm and analysis of the simulation results. It is confirmed that running time of the improved algorithm is shorter than the original algorithm.