Research On Measurement Matrix Construction Based On Compression Sensing Algorithm

The object of compressed sensing is sparse and compressible signals. The signal is the traditional sense of the sampling and compression process combined. To simplify the simulation process of digital signals, but also greatly reduces the storage requirements of the space, has great influence on the signal and image processing, has the vital significance.In this paper, on the basis of introducing the compressed sensing theory, with compressed sensing algorithm of sparse representation, measurement matrix, reconstruct the basis of the three core processes, key reconstruction algorithm are introduced in the MP and OMP algorithms. The merits of the comparison of the two kinds of algorithm performance,the experiment proved that OMP algorithm has the advantage.In order to better clarify the sparse representation of the coefficient K and the relationship of the measured value M, studies the signal sparse degree K and of general relationship between measured value M. Obtained under satisfy certain relations between them, is able to form a high probability accurately reconstruct the original signal. At the same time, introduced several kinds of commonly used measurement matrix. Detailed description of the structure and content of the commonly used measurement matrix and its as construction of measurement matrix, and then from reconstruction effect analysis of the performance of the commonly used measurement matrix.Based on the above research achievements of measurement matrix, in view of the uncertainty measurement matrix and random measurement matrix has the advantages of an improved toeplitz algorithm is put forward. According to the characteristics of the signal energy distribution at low frequency, measurement of the lower triangular matrix.In order to solve the new toeplitz matrix column and the correlation between columns, improve the performance of it as a deterministic measurement matrix. Due to the uncertainty of measurement matrix is easy to implement in the practical process of hardware, so reflected this improved prospects in application.Finally, the processing results of this paper will apply the measurement matrix in compressed sensing and the two images are reconstructed. The experimental results show that, under the Liz triangle top measurement matrix compared to Gauss measurement matrix of the image reconstruction effect is good, can better maintain the image contour and the detailed information, the reconstructed image PSNR.