Research On Optimization And Reconstruction Algorithm Of Measurement Matrix Based On Compressive Sensing

Compressed Sensing(CS)is a new emerging theory of sampling,signals are collected and compressed at the same times,breaking the traditional Nyquist sampling theorem.During CS,it is basis that signal is sparse,information of the original signal is retained as far as possible by using non-adaptive linear projection and according to numerical convex optimization,the reconstructed signal is resolved accurately.In this paper,design optimization and reconstruction algorithm in CS were studied specially,the research content is as follows:The principle of gradient descent and QR decomposition is introduced,and a new observation matrix optimization is proposed.The simulation experiment was designed on the basis of the new method and other methods,comparing different experimental results,the result of comparison shows that this optimization method has good effect in improving the peak signal to noise ratio and reconstructing stability.The principle of matrix decomposition to increase the independence of matrix columns is introduced and the correlation between the observation matrix and the sparse matrixis reduced by using the gradient descent method.Finally,these two kinds of methods are considered to improve the observation matrix.Comparing with the simulation results,it is shown that the new matrix has good reconstruction performance.A new algorithm was put forward which combines the improved observation matrix the conjugate gradient.Based on conjugate gradient reconstruction algorithm,the observation matrix is optimizedto get a new reconstruction algorithm.Compared with other algorithms,there are some same properties in new algorithm,such as: the observation matrix optimization OMP stability and robustness of the algorithm.The new property--the rigor of conjugate gradient algorithm is shown to us,which does not appear in other algorithms.According to the simulation results,it is known to us that the reconstructed time of the modified conjugate gradient algorithm is greatly reduced,and the feasibility and superiority of this new algorithmare proved.