Research On The Construction Of Compressed Sensing Matrix

Compressed sensing overcomes the constraint of the Nyquist sampling theorem,which realizes sampling and compressing signals at the same time. In compressedsensing, the sensing matrix is very important for sampling and reconstructing signals.It’s a hot and difficult problem to design good matrix which is efficient and easy toimplement on hardware. This paper proposed two improved methods to constructsensing matrix based on the deep research of the CS theory and the exiting sensingmatrices. The specific work is as follows:As the Orthogonal Symmetric Toeplitz Matrices (OSTM) has the goodcharacteristics as the random matrices, this paper put forward the construction methodof blocked OSTM based on the block circulant structure in order to resolve thephysical implementation difficulties and higher cost of the existing randommeasurement matrices.This matrix is easier for physical implementation as its pseudorandom cyclic structure. The storage and computing time can be shortened as thematrix’s independent variable number is greatly reduced. In addition, this paperproposed an adaptive blocked compressed sensing algorithm based on the blockedOSTM. Simulation results show that the proposed method can acquire higher PSNRand eliminate the block effect significantly.Recent efforts have shown that the reconstruction performance could beimproved with optimized sensing matrix according to a given dictionary for acompressed sensing (CS) system.In this paper，we further optimize the sensing matrixwhich is based on Parseval tight frame combining with the matrix decompositiontheory, so as to achieve the optimal statistical reconstruction and the optimal mutualcoherence performance at the same time. Through the approximate QR decompositionand the mean singular value decomposition (SVD), we adjust the singular values ofthe sensing matrix, so as to reduce the correlation of the matrix. A great number ofexperiments show that the proposed optimized sensing matrix realizes the minimumof the reconstructed error compared to other designs in the literature with differentsparse recovery algorithms.