Research On The Construction And Application Of Compressed Sensing Low Density Parity Observation Matrix

Compressive Sensing theory solves the bottleneck of the traditional sampling theory to the bandwidth requirement,and it can sample the signal directly while compress it.One of the most important factors in the sampling process is the measurement matrix.An excellent measurement matrix which projects the signal to the low-dimensional space should be included as much as possible the important information of original signal so that it can reconstruct the original signal more accurate.This paper studies the construction of measurement matrix of Compressive Sensing from the principle,while studying the classification of measurement matrix and the construction methods of different measurement matrix.While considering the existing problems of common measurement matrix,this paper makes improvements for the construction of measurement matrix,the details are as follows:(1)Considering the complex construction of the existing measurement matrix and its elements are not binarized,in the base of LDPC measurement matrix,a method named cascaded LDPC measurement matrix is proposed.One rule of the LDPC check matrix is that most of the columns should be incoherent to each other,which satisfied the RIP criterion of measurement matrix,so we use it as measurement matrix in Compressive Sensing.The cascaded LDPC measurement matrix is inspired by Mackay 1A construction method,which is generated by Gallager method and Mackay method together.The experimental results show that the performance of the proposed method is superior to the other methods of LDPC check matrix.(2)Considering the problem of the existing measurement matrix has large storage and not easy to implement in hardware,we combine the LDPC codes with a diagonal block matrix to generate a diagonalizable LDPC measurement matrix.Placing the same LDPC block matrix in the diagonal line not only simplify the complex construction but also can reduce the storage space.In this way,we only need to store a small number of elements of one LDPC block matrix so that we can get a whole measurement matrix.The experimental results show that the diagonalizable LDPC measurement matrix has the following advantages:a.Simple structure and fewer elements.b.High precision of image reconstruction.c.Small computation and storage.d.Easy hardware implementation.Image reconstruction simulation experiment shows that the diagonalizable LDPC matrix has a better result than the other measurement matrix and its reconstruction time is shorter.(3)Considering the particularity of the image data sampling,as well as verifying the performance of the measurement matrix,this paper designs a software system for image reconstruction based on Compressive Sensing.We can clearly understand all the process of image reconstruction in Compressive Sensing,including the sparse representation of the signal,the sampling process of the measurement matrix and the reconstruction algorithm.The software focuses on the sampling process of the measurement matrix.We can construct a measurement matrix as we need,besides that we also can see the image of measurement matrix clearly.We can more intuitive understand the measurement matrix in this way.After image reconstruction,we can see the reconstructed image as well as its evaluation index PSNR and SSIM.