The Measurement Matrix Construction And Performance Analysis In Compressed Sensing

The progress of science and technology makes the data due to be processedgrowing at an alarming rate. The traditional Nyquist sampling theorem has greatlyrestricted the ability of information processing. The appearance of compressed sensingtheory breaks this limitation. Compressed sensing theory is based on the sampling of theinformation, making the sampling process not only maintain the information of theoriginal signal, but also need far less required sampling number than that of the Nyquistsampling theorem to reconstruct the original signal precisely or approximately.This new theory attracts the attention of many scholars. As the construction ofmeasurement matrix is one of the important parts relating to the signal compression andthe accuracy of signal reconstruction, it has been the research direction of manyexcellent scholars home and abroad, which is also the focus of this article.This paper starts from the basic principle of compressed sensing and thenintroduces it in three parts. The introduction focuses on the performance requirementsand construction method of the measurement matrix, gives the RIP condition and JLlemma that the measurement matrix must satified, and by classification summarizes thecommonly used matrix. On this basis, study five types measurement matrices. First giveits specific construction method, then simulate it from the time domain signal and imagesignal, and finally analyze the performance of these types of measurement matrix. AsPartial Hadamard measurement matrix in the time domain signal and image signalsimulations shows excellent performance, it is further studied, and an improved matrixconstruction method is put forward. The simulation results show that the signalreconstruction accuracy has been greatly improved.Finding a new measurement matrix with good pe rformance and conducive tohardware implementation is the purpose of this study. However, Partial Hadamardmeasurement matrix has its own restrictions that the N must satifies N=2~K,K=1,2,3,.On the basis of the more in-depth study on the measurement matrix, associating theexcellent cross-correlation properties and pseudo-random characteristics of the Goldsequence, Gold sequence is introduced into compressed sensing to construct a Goldsequence measurement matrix. The simulation results show that this measurementmatrix has good observation effects and the hardware implementation is simple, as themeasurement matrix which is suitable for compressed sensing.