Recoverability of block-sparse signals by convex relaxation methods is considered for the underdetermined linear model. In previous works, some explicit but pessimistic recoverability results which were associated wit...Recoverability of block-sparse signals by convex relaxation methods is considered for the underdetermined linear model. In previous works, some explicit but pessimistic recoverability results which were associated with the dictionary were presented. This paper shows the recoverability of block-sparse signals are associated with the block structure when a random dictionary is given. Several probability inequalities are obtained to show how the recoverability changes along with the block structure parameters, such as the number of nonzero blocks, the block length, the dimension of the measurements and the dimension of the block-sparse representation signal. Also, this paper concludes that if the block-sparse structure can be considered, the recoverability of the signals wil be improved. Numerical examples are given to il ustrate the availability of the presented theoretical results.展开更多
This paper presents a new subband adaptive filter(SAF)algorithm for system identification scenario under impulsive interference,named generalized continuous mixed p-norm SAF(GCMPN-SAF)algorithm.The proposed algorithm ...This paper presents a new subband adaptive filter(SAF)algorithm for system identification scenario under impulsive interference,named generalized continuous mixed p-norm SAF(GCMPN-SAF)algorithm.The proposed algorithm uses a GCMPN cost function to combat the impul-sive interference.To further accelerate the convergence rate in the sparse and the block-sparse system identification processes,the proportionate versions of the proposed algorithm,the L0-norm GCMPN-SAF(L0-GCMPN-SAF)and the block-sparse GCMPN-SAF(BSGCMPN-SAF)algorithms are also developed.Moreover,the convergence analysis of the proposed algorithm is provided.Simulation results show that the proposed algorithms have a better performance than some other state-of-the-art algorithms in the literature with respect to the convergence rate and the tracking capability.展开更多
In this paper,we investigate truncated l2\l1-2 minimization and its associated alternating direction method of multipliers(ADMM)algorithm for recovering the block sparse signals.Based on the block restricted isometry ...In this paper,we investigate truncated l2\l1-2 minimization and its associated alternating direction method of multipliers(ADMM)algorithm for recovering the block sparse signals.Based on the block restricted isometry property(Block-RIP),a theoretical analysis is presen ted to guarantee the validity of proposed method.Our theore tical resul ts not only show a less error upper bound,but also promote the former recovery condition of truncated l1-2 method for sparse signal recovery.Besides,the algorithm has been compared with some state-of-the-art algorithms and numerical experiments have shown excellent performances on recovering the block sparse signals.展开更多
基金supported by the International Cooperation Project of Guangdong Natural Science Fund(2009B050700020)the Natural Science Foundation of China-Guangdong Natural Science Foundation Union Project(U0835003)
文摘Recoverability of block-sparse signals by convex relaxation methods is considered for the underdetermined linear model. In previous works, some explicit but pessimistic recoverability results which were associated with the dictionary were presented. This paper shows the recoverability of block-sparse signals are associated with the block structure when a random dictionary is given. Several probability inequalities are obtained to show how the recoverability changes along with the block structure parameters, such as the number of nonzero blocks, the block length, the dimension of the measurements and the dimension of the block-sparse representation signal. Also, this paper concludes that if the block-sparse structure can be considered, the recoverability of the signals wil be improved. Numerical examples are given to il ustrate the availability of the presented theoretical results.
文摘This paper presents a new subband adaptive filter(SAF)algorithm for system identification scenario under impulsive interference,named generalized continuous mixed p-norm SAF(GCMPN-SAF)algorithm.The proposed algorithm uses a GCMPN cost function to combat the impul-sive interference.To further accelerate the convergence rate in the sparse and the block-sparse system identification processes,the proportionate versions of the proposed algorithm,the L0-norm GCMPN-SAF(L0-GCMPN-SAF)and the block-sparse GCMPN-SAF(BSGCMPN-SAF)algorithms are also developed.Moreover,the convergence analysis of the proposed algorithm is provided.Simulation results show that the proposed algorithms have a better performance than some other state-of-the-art algorithms in the literature with respect to the convergence rate and the tracking capability.
基金The authors would like to thank reviewers for valuable comments.This work was supported by Natural Science Foundation of China(Grant Nos.61673015,61273020)Fundamental Research Funds for the Central Universities(Grant Nos.XDJK2015A007,XDJK 2018C076,SWU1809002).
文摘In this paper,we investigate truncated l2\l1-2 minimization and its associated alternating direction method of multipliers(ADMM)algorithm for recovering the block sparse signals.Based on the block restricted isometry property(Block-RIP),a theoretical analysis is presen ted to guarantee the validity of proposed method.Our theore tical resul ts not only show a less error upper bound,but also promote the former recovery condition of truncated l1-2 method for sparse signal recovery.Besides,the algorithm has been compared with some state-of-the-art algorithms and numerical experiments have shown excellent performances on recovering the block sparse signals.
