Recovery Algorithms Of Block Sparse Signal Based On Compressed Sensing And It's Applications

Compressed sensing is the most popular research direction in the field of signal processing in recent years.The signal sampling by compressed sensing is proceeded with sampling rate less than the demand of Nyquist sampling theorem.Compressed sensing opens up a new road in solving the bottle neck problem of data redundancy and resource-wasting,and provides a new opportunity of the development of other subjects.As one of the crucial issues,the reconstruction algorithm plays a key role in the application of compressed sensing and affects its practical usage.Since compressed sensing was presented,how to design the algorithm with low complexity,high reconstruction quality has been the focus of research.Different from general sparse signals in conventional sense,some real-world signals may exhibit some additonal structures,i.e.the non-zero coefficents appear in a few fixed blocks,we refer to these signals as block sparse signals.Such block sparse signals arise in various application problems,say,DNA microarray,face recognition,electrocardiography signal,color imaging,etc.Since the block sparse signals are a special case of sparse signal,the reconstruction of block sparse signals can be processed with classical compressed sensing reconstruction algorithms.However,if the internal structure of the block sparse signals is ignored,it will greatly affects the efficiency of reconstruction algorithms.Based on the theory of compressed sensing,this thesis focuses on the reconstruction algorithm of block sparse signals and it's applications,the main works are summarized as follows:1.Based on the smoothed?₀ norm?SL0?algorithm,a generalized gaussian function?GGFSL0?algorithm is proposed.This algorithm can be regarded as the generalization of SL0 algorithm,which uses generalized Gaussian function?GGF?instead of Gaussian function.The GGFSL0 algorithm utilizes generalized Gaussian functions to approach the?₀ norm and transforms the non-convex optimization problem into the convex optimization problem,and then maximizes it by using gradient descent method.Simulations with synthetic data show that the proposed approach achieves improved sources estimation performance with respect to different parameters,sparsity,noise,and dimension.2.On the basis of block smoothed?₀ norm?BSL0?algorithm,an improved block smoothed?₀ norm?IBSL0?algorithm for block sparse signal is proposed.The smoothed Gaussian functions is substituted by inverse tangent function,the convergence equality is further improved by optimizing the decreasing factor.Numerical experiments show that the IBSL0 algorithm not only has good robustness,and compared with other algorithms,the signal-to-noise ratio is improved in the case of different block size.3.Based on the generalized orthogonal matching pursuit?gOMP?algorithm,a block generalized orthogonal matching pursuit?BgOMP?algorithm is proposed for block sparse signals.In this algorithm,multiple block atoms are selected for the final support set in each iteration to improve the efficiency of the estimation support set.In addition,the sufficient conditions for the exact recovery condition are discussed by using the restricted isometry property?RIP?.In the numerical experiment,we study the effect on the reconstruction performance with respect to different number of block index selected in each iteration,and discuss the change of the algorithm's reconstruction performance in the light of Gaussian block sparse signals and binary block sparse signals as block sparsity and the number of measurement vary.Reconstruction experiment with synthetic signal and speech signal,image signal?seismic signal show that the algorithm has good estimation euqality.4.For the problem of block sparse signal reconstruction,a block backtracking-based adaptive OMP?BBAOMP?algorithm is proposed.The BBAOMP algorithm adds a backtracking step to refine the estimated support set by deleting the wrong block indices selected at the previous stage.Owing to the backtracking step,the BBAOMP algorithm provides double checks of the chosen atom's reliability,which yields much better sparse reconstruction performance.Another outstanding advantage of BBAOMP algorithm is that it does not require the sparsity level to be known as a prior.Numerical experiment studies the effect on the reconstruction performance with respect to different number of block index selected in each iteration,and discuss the change of the algorithm's reconstruction performance in the light of Gaussian block sparse signals and binary block sparse signals as block sparsity and the number of measurement vary.Reconstruction experiment with synthetic signal and speech signal,image signal?seismic signal show that the algorithm has good estimation euqality.5.As to the problem of block sparse signal reconstruction,a distributed compressed sensing reconstruction algorithm based on BAOMP algorithm is proposed,which is called DCSBBAOMP algorithm.This algorithm can recover multichannel block sparse signals at the same time,and don't need the sparsity of each signal as a prior.Considering the common support-set model,numerical experiment is used to discuss the change of the algorithm's reconstruction performance as the sparsity and the number of measurement varied.In addition,we study the effect on the reconstruction performance without the prior of block size d,experimental results show that even we don't know the block size of block sparse signal in advance,we may get better reconstruction result by adjusting the block size in our algorighm.