Research On Construction Methods Of Convolution Compressed Sensing Measurement Matrices

Compressed sensing is a new signal processing technology which has emerged in recent years,It samples the signal at a sampling frequency far lower than the sampling theorem and combines signal sampling and compression.Convolution compressed sensing is a method uses semi deterministic cyclic matrix as measurement matrix.The measurements are obtained by using the circulate convolution signal of the deterministic sequence and then by random subsampling.This thesis mainly studies the constructions of measurement matrices.Random measurement matrix is a kind of measurement matrices with excellent performance,which can recover signal with great probability.However,the random measurement matrix needs a large amount of store space in practical application,and it is difficult to implement by hardware.Therefore,this thesis focus on constructing of deterministic measurement matrices which needs a small amount of store space and is easy to implement by hardware.Firstly,a method of constructing deterministic measurement matrix based on cyclotomic classes of second order is proposed.Based on the cyclotomic class of finite field,a class of sequences with conjugate symmetry is constructed.The binary transformation,Fourier inverse transformation and cyclic shift are used to generate the matrix.The rows of the matrix are randomly selected to generate the measurement matrix of all real coefficients.The correlation of the resultant sequence is calculated by mathematical method,which ensures the certainty of construction and the low correlation of measurement matrix.Through the experimental simulation of one-dimensional signal and two-dimensional image,the measurement matrix based on cyclotomic classes of second order has better performance of recovering sparse signals than other measurement matrices.Secondly,a method of constructing the deterministic measurement matrix based on cyclotomic classes of higher order is proposed.The matrix is a generalization of cyclotomic matrix of second order,and more parameter measurement matrix can be obtained.By using computer-aided tools to calculate the correlation of sequences,the low correlation of the constructed high order cyclotomi matrix is verified by computer analysis.The simulation results show that the performance of the measurement matrix based on higher order cyclotomic class is better than that of the random measurement matrix.Finally,the measurement matrix based on the cyclotomic classes is used as pilot sequence in the field of channel estimation.By analyzing the MIMO system model and comparing with the CS theory system model,the constructed matrix can be used as the pilot sequence in channel estimation to calculate the channel impulse response.Simulation results show that the measurement matrix based on cyclotomic class has better performances compare with the measurement matrix constructed by known sequences,the estimation value of signal estimation is more accurate.