Construction And Optimization Of Binary Measurement Matrix For Compressed Sensing

Compressed sensing theory is a very popular signal acquisition and processing theory in recent years. For sparse or compressible signal, the compressed sensing theory’s sampling rate for data acquisition is far below than the Nyquist theorem. And the theory can accuratley reconstruct the original signal in a big probability. Single pixel imaging system is a hot area in the application of compressed sensing theory and its measurement matrix should be binary. To solve the problem of the reconstruction performance of the existing binary measurement matrix and the negative correlation from hardware implementation, a new strategy of constructing matrix is proposed. The performance of the strategy is verified by simulation.Firstly, based on the construction method of structured block diagonal matrix, and the balanced orthogonal Gold sequence in the spreading sequence, a pseudo-random block diagonal measurement matrix is designed in this dissertation. This matrix retains the good irrelevance and easy-hardware implementation of balanced orthogonal Gold sequence. It breaks through the original sequence size so that more different size of standard images can be compressived, sampled and reconstructted. In particular, the measurement matrix can be divided into blocks to reconstruct the signal, which greatly improves the reconstruction rate in the case that the reconfiguration performance is basically unchanged. Simulation results show that the measurement matrix has a good performance.Then, considering the single pixel imaging system for binary measurement matrix, and combining with the existing orthonogal malization of row vectors optimization algorithm, this dissertation presents a matrix separation construction algorithm. The similar matrix constructed by this algorithm is similar to the properties of optimize matrices. A simple binary measurement matrix which can be easily implemented in hardware is used by this dissertation at the sampling stage. Similarly, a similar matrix of better reconstruction performance is used by this dissertation at the reconstruction stage. Theoretical analysis and experimental results show that the reconstruction performance of the proposed strategy is better than the original matrix.