Research On Sparse Representation And Reconstruction For Block-structured Signal Based On Compressive Sensing

Block-sparse signal is a kind of sparse signal with special structure,namely the nonzero entries in the sparse signal appeared in blocks.In practical applications,such as multiband signals,face,motion target and so on can be viewed as block-sparse signals.The block-sparse singal expand the scope of application of the Compressive Sensing,and we can take full advantage of intrinsic-structure information of singal effectively.This thesis focus on learning block-structured dictionary based on the sensing matrix optimization,designing effective reconstruction algorithm and solving the problems when we apply the theory of block-sparse signal to practical applications.Main works are as follows:1.An algorithm for block-structured dictionary-learning and sensing matrix optimization based on Equiangular Tight Frame(ETF) is proposed.Taking ETF as the ultimate aim,we can design the sensing matrix to make the coherence of equivalent block dictionary approach to theoretical minimum-welch bound,and we propose a learning method to optimize the block-structured dictionary to get a effective block-sparse representation of the signal simultaneously.During learning the block-structure dictionary,we introduce the idea of matrix decomposition to replace KSVD algorithm,so we can overcome problems that the KSVD algorithm converges to a local minimum and updates block-structured dictionary is of high computational complexity. Experiments show that,compared with KSVD algorithm,BKSVD algorithm,BKSVD_ETF algorithm,CBKSVD_ETF algorithm,the proposed algorithm can averagely improve PSNR by 4.4185 dB,1.6865 dB,1.6706 dB,0.6368 dB respectively,and the time cost of block dictionary-learning is reduced by about sixty percent compared with CBKSVD_ETF algorithm.2.Introducing a subspace backtracking block orthogonal matching pursuit algorithm based on sensing matrix optimization(SMOB-BOMP).Under the help of ETF,we can design the sensing matrix to improve the performance of BOMP algorithm.To avoid problems that the BOMP algorithm can only select the optimal atoms for current iteration and the selected false atoms cann’t be self-corrected in the subsequent iterations,we embed the BSP algorithm which can solve above problems into the procedure of BOMP algorithm to get the global optimum solution.The experiments of images reconstruction show that,compared with BOMP algorithm,BSP algorithm,B-BOMP algorithm,SBOMP algorithm,the proposed SMOB-BOMP algorithm can averagely improve PSNR by 4.0481 dB,2.9054 dB,2.1020 dB,0.8515 dB respectively.3. In order to handle the block-structure sparse multiband signal in the Modulated Wideband Converter(MWC) more effectively,two improvements are proposed:a)To avoid the unstability and large storage space produced by random measurement matrix,we construct a generally deterministic and lower triangular circulant measurement matrix to overcome above problems and the performance of sampling and reconstruction will not be reduced at the same time;b)In the process of atoms matching of recovery algorithm,we introduce a vector made up of normalizing factors to avoid the influence caused by ignoring normalization of columns of the measurement matrix,and we can select a pair of optimal atoms in the process of atoms matching of every iteration by making use of conjugated-symmetrical property of the column vectors of measurement matrix.Experiments show that the proposed method can improve the performance of sampling and reconstruction effectively.