Block multiple measurement vectors (BMMV) is a reconstruction algorithm that can be used to recover the support of block K-joint sparse matrix X from Y = ΨX + V. In this paper, we propose a sufficient condition for a...Block multiple measurement vectors (BMMV) is a reconstruction algorithm that can be used to recover the support of block K-joint sparse matrix X from Y = ΨX + V. In this paper, we propose a sufficient condition for accurate support recovery of the block K-joint sparse matrix via the BMMV algorithm in the noisy case. Furthermore, we show the optimality of the condition we proposed in the absence of noise when the problem reduces to single measurement vector case.展开更多
In finite element analysis(FEA),optimizing the storage requirements of the global stiffness matrix and enhancing the computational efficiency of solving finite element equations are pivotal objectives.To address these...In finite element analysis(FEA),optimizing the storage requirements of the global stiffness matrix and enhancing the computational efficiency of solving finite element equations are pivotal objectives.To address these goals,we present a novel method for compressing the storage of the global stiffness matrix,aimed at minimizing memory consumption and enhancing FEA efficiency.This method leverages the block symmetry of the global stiffness matrix,hence named the blocked symmetric compressed sparse column(BSCSC)method.We also detail the implementation scheme of the BSCSC method and the corresponding finite element equation solution method.This approach optimizes only the global stiffness matrix index,thereby reducing memory requirements without compromising FEA computational accuracy.We then demonstrate the efficiency and memory savings of the BSCSC method in FEA using 2D and 3D cantilever beams as examples.In addition,we employ the BSCSC method to an engine connecting rod model to showcase its superiority in solving complex engineering models.Furthermore,we extend the BSCSC method to isogeometric analysis and validate its scalability through two examples,achieving up to 66.13%memory reduction and up to 72.06%decrease in total computation time compared to the traditional compressed sparse column method.展开更多
In many practical applications,we need to recover block sparse signals.In this paper,we encounter the system model where joint sparse signals exhibit block structure.To reconstruct this category of signals,we propose ...In many practical applications,we need to recover block sparse signals.In this paper,we encounter the system model where joint sparse signals exhibit block structure.To reconstruct this category of signals,we propose a new algorithm called block signal subspace matching pursuit(BSSMP)for the block joint sparse recovery problem in compressed sensing,which simultaneously reconstructs the support of block jointly sparse signals from a common sensing matrix.To begin with,we consider the case where block joint sparse matrix X has full column rank and any r nonzero rowblocks are linearly independent.Based on these assumptions,our theoretical analysis indicates that the BSSMP algorithm could reconstruct the support of X through at most K-r+[r/L]iterations if sensing matrix A satisfies the block restricted isometry property of order L(K-r)+r+1 with δB_(L(K-r)+r+1)<max{√r/√K+r/4+√r/4,√L/√Kd+√L}.This condition improves the existing result.展开更多
We consider the block orthogonal multi-matching pursuit(BOMMP) algorithm for the recovery of block sparse signals.A sharp condition is obtained for the exact reconstruction of block K-sparse signals via the BOMMP algo...We consider the block orthogonal multi-matching pursuit(BOMMP) algorithm for the recovery of block sparse signals.A sharp condition is obtained for the exact reconstruction of block K-sparse signals via the BOMMP algorithm in the noiseless case,based on the block restricted isometry constant(block-RIC).Moreover,we show that the sharp condition combining with an extra condition on the minimum l_2 norm of nonzero blocks of block K-sparse signals is sufficient to ensure the BOMMP algorithm selects at least one true block index at each iteration until all true block indices are selected in the noisy case.The significance of the results we obtain in this paper lies in the fact that making explicit use of block sparsity of block sparse signals can achieve better recovery performance than ignoring the additional structure in the problem as being in the conventional sense.展开更多
文摘Block multiple measurement vectors (BMMV) is a reconstruction algorithm that can be used to recover the support of block K-joint sparse matrix X from Y = ΨX + V. In this paper, we propose a sufficient condition for accurate support recovery of the block K-joint sparse matrix via the BMMV algorithm in the noisy case. Furthermore, we show the optimality of the condition we proposed in the absence of noise when the problem reduces to single measurement vector case.
基金supported by the National Natural Science Foundation of China(Grant No.52075184)Guangdong Basic and Applied Basic Research Foundation,China(Grant No.2024A1515011786).
文摘In finite element analysis(FEA),optimizing the storage requirements of the global stiffness matrix and enhancing the computational efficiency of solving finite element equations are pivotal objectives.To address these goals,we present a novel method for compressing the storage of the global stiffness matrix,aimed at minimizing memory consumption and enhancing FEA efficiency.This method leverages the block symmetry of the global stiffness matrix,hence named the blocked symmetric compressed sparse column(BSCSC)method.We also detail the implementation scheme of the BSCSC method and the corresponding finite element equation solution method.This approach optimizes only the global stiffness matrix index,thereby reducing memory requirements without compromising FEA computational accuracy.We then demonstrate the efficiency and memory savings of the BSCSC method in FEA using 2D and 3D cantilever beams as examples.In addition,we employ the BSCSC method to an engine connecting rod model to showcase its superiority in solving complex engineering models.Furthermore,we extend the BSCSC method to isogeometric analysis and validate its scalability through two examples,achieving up to 66.13%memory reduction and up to 72.06%decrease in total computation time compared to the traditional compressed sparse column method.
基金partially supported by the Natural Science Foundation of Henan Province(Grant Nos.252300420326,242300420252)in part by the Key Scientifc Research Project of Colleges and Universities in Henan Province(Grant No.24A120007)+1 种基金in part by Training Program for Young Backbone Teachers in Higher Education Institutions of Henan Province(Grant No.2023GGJS037)in part by the National Natural Science Foundation of China(Grant Nos.12271215,12326378 and 11871248)。
文摘In many practical applications,we need to recover block sparse signals.In this paper,we encounter the system model where joint sparse signals exhibit block structure.To reconstruct this category of signals,we propose a new algorithm called block signal subspace matching pursuit(BSSMP)for the block joint sparse recovery problem in compressed sensing,which simultaneously reconstructs the support of block jointly sparse signals from a common sensing matrix.To begin with,we consider the case where block joint sparse matrix X has full column rank and any r nonzero rowblocks are linearly independent.Based on these assumptions,our theoretical analysis indicates that the BSSMP algorithm could reconstruct the support of X through at most K-r+[r/L]iterations if sensing matrix A satisfies the block restricted isometry property of order L(K-r)+r+1 with δB_(L(K-r)+r+1)<max{√r/√K+r/4+√r/4,√L/√Kd+√L}.This condition improves the existing result.
基金National Natural Science Foundation of China(Grant Nos. 11271050 and 11371183)
文摘We consider the block orthogonal multi-matching pursuit(BOMMP) algorithm for the recovery of block sparse signals.A sharp condition is obtained for the exact reconstruction of block K-sparse signals via the BOMMP algorithm in the noiseless case,based on the block restricted isometry constant(block-RIC).Moreover,we show that the sharp condition combining with an extra condition on the minimum l_2 norm of nonzero blocks of block K-sparse signals is sufficient to ensure the BOMMP algorithm selects at least one true block index at each iteration until all true block indices are selected in the noisy case.The significance of the results we obtain in this paper lies in the fact that making explicit use of block sparsity of block sparse signals can achieve better recovery performance than ignoring the additional structure in the problem as being in the conventional sense.
