The Method And Application Of Prm Compressed Sensing

Compressed sensing theory has attracted wide attention of scholars at home and abroad since proposed. With the development of the theory, it has been applied in many fields, especially having rapid development in signal processing field. At present, domestic and foreign researchers have got a lot of achievements in compressed sensing, but in the area of theory development, there are still many problems to be solved, such as hardware implementation-unfriendly, no best perceived performance, poor universality and so on. Aiming at the above problems, this paper expand study in the constraints compressed sensing measurement matrices satisfied, the construction of measurement matrix, reconstruction algorithms, and all of which are applied in one dimensional industry signals and image signals. The main work is as follows:Firstly, this paper introduced the Nyquist sampling theory and compressed sensing theory, which has broken the bottleneck of Nyquist, and it also gives the situation at home and abroad of the key part of compressed sensing, i.e. measurement matrix, and the applications of compressed sensing. Discussing the measurement matrix of compressed sensing satisfies the constraint condition, such as Restricted Isometry Property and Gerschgorin disk theorem. At the same time, this paper introduces the structure of several measurement matrices and the process of the reconstruction algorithms.Secondly, in further study of four application principles in construction of measurement matrix, according to exsited measurement matrices, we propose a new form of measurement matrix called Pseudo-random measurement (PRM) matrix for compressive sensing. The proposed matrix is constructed by the structured approach with balanceable Gold sequence diagonal matrix, Walsh-Hadamard matrix, and the down-sampling matrix. It combines the internal advantages of random measurement matrix and the deterministic binary measurement matrix. More specifically, PRM matrix can provide good reconstruction performance with low computational complexity. And combining PRM matrix with different reconstruction algorithms applied to industry signals and image signals. Experimental results of1D power quality signals, pipeline leakage signal and2D natural images demonstrate that the proposed matrix outperforms other traditional measurement matrices, such as Gaussian matrix, Bernoulli matrix, and Toeplitz matrix.Finally, through the improvement of PRM measurement matrix, block PRM measurement matrix, namely BPRM matrix was proposed. The mathematical derivation and analysis show that BPRM satisfies RIP, which can be used as compressed sensing measurement matrix. And BPRM was applied to1D power quality signals and2D image signals. Through simulation experiments of power quality signal with different block BPRM matrix.64×64BPRM matrix is applied to five standard test images. The experimental data show that different block BPRM matrices have similar reconstruction results, which could reconstruct power quality signals and images accurately.