Research On Compressed Sensing Algorithms Based On Different Prior Information

Compressed Sensing(CS)theory is a new framework that can successfully sample and compress signals at the same time,and accurately reconstruct the original signal under the premise of the unique structure of the sparse model,with much lower sampling rate than that required by the traditional Nyquist sampling theorem It exhibits a distinct advantage for processing 1-D and 2-D signals.In CS,the selection of suitable prior information seriously affects the quality of CS reconstruction.Currently,most of the existing compressed sensing techniques mainly deal with the linear situation,however,many signals,especially images,videos,etc.,are usually observed with high dimensionality,variability and complexity.Therefore,it is difficult to obtain the desired sparsity via linear representation models,needing to extend to a nonlinear manifold to obtain a better sparse representation.Besides,in most practical applications,it is difficult to know the prior information of signals in advance.Hence,this paper mainly studies the compressed sensing algorithms based on different prior information,the main innovative points are as follows:(1)A compressed sensing algorithm based on AK-BRP dictionary learning(AK-BRP-CS)is proposed.In the case that the prior information of the signal is known and is a linear sparsity priori,an adaptive K-BRP dictionary learning algorithm(AK-BRP)is firstly proposed to make up for K-SVD algorithm,since K-SVD algorithm has large computational cost and slow running speed.Secondly,the AK-BRP dictionary learning algorithm is used in CS for the sparse representation of video frames.Comparative simulation experimental results of several test video frames with a variety of sampling ratios have demonstrated that the proposed algorithm has better reconstruction performance and faster operation.(2)A Kernel compressed sensing algorithm based on AKKSVD kernel dictionary learning(AKKSVD-KCS)is proposed.In the case that the prior information of the signal is known and is a nonlinear sparsity priori,an adaptive kernel K-SVD dictionary learning algorithm(AKKSVD)is firstly proposed to achieve sparse representation of video frames under nonlinear manifolds.Secondly,the kernel dictionary,trained by AKKSVD algorithm,is used in kernel compressed sensing theory for the kernel sparse representation of video frames.Comparative simulation experimental results of several test video frames with a variety of sampling ratios have demonstrated that the proposed algorithm displays high efficiency for the reconstruction of non-linear signals.(3)A blind compressed sensing algorithm based on adaptive double sparsity dictionary learning(ADS-BCS)is proposed.In the case that the prior information of the signal is unknown,in this paper,in view of the existing blind compressed sensing(BCS)theory,a novel blind compressed sensing framework based on split Bregman iteration(SBI)is proposed to simultaneous video frame recovery and dictionary learning directly from CS measurements,by constraining the dictionary as a double sparsity dictionary structure.Comparative simulation experimental results of several test video frames with a variety of sampling ratios have demonstrated that the proposed algorithm can achieve blind reconstruction of video frames more effectively,and has higher reconstruction accuracy.