The Research Of Compressive Sensing Algorithm For Dynamic Signal

Dynamic Compressive Sensing(DCS)has been a research hotspot in the field of signal processing since 2008,and is designed to deal with sparse signals which signal's support sets slowly change with time.However,the existing dynamic compression sensing only considers the signal's support set changes with time,but does not take into account the variation of the signal's sub-band bandwidth.In this thesis,the following three points of dynamic performance of the signal are considered:(1)the coordinate of the signal's support set changes dynamically with time;(2)the amplitude of the signal' s support set changes dynamically with time;(3)the sub-band bandwidth of the signal changes with time.To improve the anti-jamming performance of the reconstruction algorithm and the wide range of applications as starting points,this thesis focuses on the analysis of its recovery algorithm.The main contributions of this thesis are as follows:(1)Aiming at the problem that the signal recovery accuracy is reduced due to the spectrum leakage by the signal processing method in the traditional compression sensing recovery algorithm.In this thesis,we consider a practical multi-band streaming signal,and propose a modulated Discrete Prolate Spheroidal Sequence(DPSS)to sparsely represent multi-band signals to avoid spectrum leakage.The simulation compare the sparse representation of the same multi-band signal under DFT basis and DPSS basis respectively.The results show that sparsity of multi-band signals under DPSS basis avoids spectrum leakage.(2)Considering the three-point dynamic characteristics of time-varying signals,a multi-band sparse signal model is proposed by using the signal's correlation in the time domain.Based on this model,a multi-band signal adaptive restoration algorithm is proposed.At present,the known methods all assume that the signal noise is known and the signal sparsity has some constraints.In order to solve this problem,we consider the intrinsic relationship between the signals and estimate the signal's support set and noise in the recovery process.This thesis presents a dynamic signal noise adaptive estimation algorithm.Simulation results show that the proposed algorithm improves the recovery accuracy of multi-band signals under high compression rate.(3)For the dynamic sparse signal,in addition to taking into account the joint sparseness of the signal time-frequency characteristics,this thesis also takes into account the isomorphism between the multi-source signals in space nodes.Starting from two multi-source time-varying signal scenarios:1)The topological structure of the graph signal does not change with time,but the signal value of each source point changes slowly with time;2)The topological structure of the graph signal changes with time.Combining the timing dynamics of the signal with the theory of kernel reconstruction,Kernel Kalman Filter(KKF)algorithm based on Kalman filter is proposed.And this thesis constructs two kinds of kernels to capture the space-time information corresponding to the above two scenarios.At the same time,this thesis implements two-dimensional compression in space and time.