Research On Signal Recovery Algorithms Based On Compressed Sensing Theory

In the traditional signal sampling process,Nyquist sampling theorem must be satisfied for preventing signal distortion.But in some practical applications such as video and image processing,an increased sampling frequency will substantially increase large volume data transmission and storage costs.In recent years,an emerging novel theory of signal acquirement——Compressive sensing(CS)provides a good opportunity for solving this problem.Different from the traditional signal acquisition process,compressive sensing is based on the compressibility of the signal.It captures compressible signals at a sampling rate significantly below the Nyquist rate.It first employs non-adaptive linear projections that preserve the information of the signal,and then using optimization methods from these projections accomplished the signal reconstruction.At present,Compressive sensing has broad applications such as compressive imaging,blind source separation,biomedical,etc.This dissertation focus on the problems of Compressive sensing recovery algorithms,and the main content can be summarized as:(1)Considering non-adaptability of traditional greedy algorithm,when adopt these algorithms to recover sparse signal,they need to use apriori information sparsity level as input parameter.So Compressive Sampling Modifying Matching Pursuit(CoSaMMP)is proposed in this paper.CoSaMMP adopted fuzzy threshold preliminary rule with theoretical guarantee to avoid using apriori information of signals in primary election phase,set the initial pruning threshold to reduce unnecessary iterations,improved the pruning mode to enhance the recovery accuracy and avoid using apriori information of signals in pruning phase,finally realized adaptive recovery for compressible signals.Simulated results show that for the same sparsity level,the operation speed of CoSaMMP increased by 2 fold compared with Compressive Sampling Matching Pursuit(CoSaMP),and the required measurement number decreases about 1%,In addition under the conditions of the high sparsity level,the algorithm have better anti-interference ability than CoSaMP.(2)Since the output index-set of the traditional greedy pursuit algorithms contain many redundant indexes and these algorithms didn’t consider the impact of noise on Algorithm Performance.In order to improve recovery Performance of the traditional greedy algorithms.Bayesian hypothesis Testing Match Pursuit(BTMP)algorithm is proposed.Firstly,this algorithm presents a Bayesian hypothesis testing model which is used to identify the indexes of nonzero elements of sparse signal in the noisy case.Secondly,the output index-set of pursuit algorithm is used as the candidate set of this mode,and then every element of the set is tested to eliminate redundant indexes.Finally,the evaluation of sparse signal is reconstructed from the eliminated indexes set by least-squares algorithm.Simulated results show that in the same conditions,BTMP algorithm has no redundant indexes,and shows better anti-jamming ability and recovery accuracy than those of the traditional greedy algorithms.(3)The traditional greedy pursuit methods only consider the atoms having the highest correlation with the residual signal.So these algorithms have inherent defects.When an unknown sparse signal has a high dynamic range,it usually can’t be exactly recovered by the traditional greedy pursuit algorithms.The main reason is that a few smaller amplitude elements of sparse signal can’t be recovered.In order to improve reconstruction dynamic range and weaken the impact of smaller amplitude elements on reconstruction performance of greedy pursuit,Maximal-Minimal Correlation atoms Algorithm(Max-MinCA)is proposed in this paper.It not only considers the higher correlation atoms,but also reserves the lower ones with the residual signal.Due to reserving the lower correlation atoms,it naturally brings in some of redundant atoms.In Max-MinCA,Bayesian Pursuit algorithm is adopted to eliminate them.Numerical experiments show that Max-MinCA can improve reconstruction dynamic range and reconstruction accuracy.It also has better noise immunity.(4)Once smoothed l0-norm(SLO)algorithm is used,the recovery signals always cause burrs.And its parameter σmm needs to be set by user.When magnitude of non-zero elements in sparse signal is very small,the sparse signal usually can not exactly recovery by SL0 owing to unreasonable setting σmin,In order to solve above-mentioned problems,a Modified smoothed l0-norm(ML0)algorithm is proposed in this paper.The algorithm based on Bernoulli-Gaussian model to estimate orders of magnitude ofσmin and set σmin automatically.Then the algorithm adopt the estimated σmin as threshold toeliminate burrs.Simulated results show that MLO have not any burr compared with SL0.and the estimated σmin can effectively avoid not exactly recovery case owing to magnitude of non-zero elements in sparse signal is very small.(5)Through analyzing on conjugate gradient pursuit(CGP)and stagewise weak selection conjugate gradient pursuit(StWCGP),the recovery accuracy of these two algorithms can be further promoted.In order to improve recovery performance,a stagewise weak selection modifying approximation conjugate gradient pursuit(StWMCGP)algorithm was proposed in this paper.This algorithm modified the direction in the directional pursuit algorithm and clearly presented a stopping criterion to search the indices of elements and get an index-set.Then the evaluation of sparse signal was obtained by using Least-squares algorithm and the obtained index-set.Numerical experiments confirm the validity of our method.