Construction Method And Performance Study Of Measurement Matrix Based On Compressive Sensing

Compressive sensing is a new theory insignal processing, which can complete signal sampling and compression at the same time. The requiredsignal sampling frequency of compressive sensing is much less than the Nyquist sampling frequency. What is more, we can reconstruct the original signal through a nonlinear method.The proposed compressive sensing provides the basic theoretical and academic ideas to break through the limits of Nyquist sampling frequency. The study primarily includes: signal sparse representation, measurement matrix design and signal reconstruction. As an important part of compressive sensing, measurement matrix directly influences the signal reconstruction precision and the physical feasibility of compressive sensing.At present, most of measurement matrixes still have some problems. For example, random measurement matrixesare not easy to realize on the hardware and the performance ofthe toeplitz measurement matrix is not very well. In order to improve the performanceof measurement matrixes and develop the compressive sensing theory, so firstly, the paper starts from the basic theory of compressive sensing, RIP requirement and the construction method of the measurement matrix. Then it introduces several measurement matrixes which are widely used, including those measurement matrixes design methods and theiradvantages and disadvantages. At the same time, we use a one-dimension signal and a 2-dimension image signal to test and compare the performanceof those measurement matrixes with differentmeasurement values.Secondly, a random measurement matrix is not easy to realize on the hardware, so we use logistic mapping method to produce a pseudo-random sequence to design a measurement matrix. The measurement matrix not only remains the randomness but also increases the certainty at the same time. The simulations show that the performance of the proposed measurement matrix is nearly the same as those random measurement matrixes, such as the gauss random measurement matrix,and the proposed measurement matrix is easier to realize on the hardware.In the end, in order to solve the lacking randomness of the toeplitz measurement matrix, a super prime-number-based method is introducedto generate the pseudo sequence to construct the elements of the toeplitz measurement matrix. The simulations show the measurement matrix’s performance is improved,furthermore, it is easy to realize on the hardware and has stable performance.