The order of the projection in the algebraic reconstruction technique(ART)method has great influence on the rate of the convergence.Although many scholars have studied the order of the projection,few theoretical proof...The order of the projection in the algebraic reconstruction technique(ART)method has great influence on the rate of the convergence.Although many scholars have studied the order of the projection,few theoretical proofs are given.Thomas Strohmer and Roman Vershynin introduced a randomized version of the Kaczmarz method for consistent,and over-determined linear systems and proved whose rate does not depend on the number of equations in the systems in 2009.In this paper,we apply this method to computed tomography(CT)image reconstruction and compared images generated by the sequential Kaczmarz method and the randomized Kaczmarz method.Experiments demonstrates the feasibility of the randomized Kaczmarz algorithm in CT image reconstruction and its exponential curve convergence.展开更多
Tikhonov regularization is a powerful tool for solving linear discrete ill-posed problems.However,effective methods for dealing with large-scale ill-posed problems are still lacking.The Kaczmarz method is an effective...Tikhonov regularization is a powerful tool for solving linear discrete ill-posed problems.However,effective methods for dealing with large-scale ill-posed problems are still lacking.The Kaczmarz method is an effective iterative projection algorithm for solving large linear equations due to its simplicity.We propose a regularized randomized extended Kaczmarz(RREK)algorithm for solving large discrete ill-posed problems via combining the Tikhonov regularization and the randomized Kaczmarz method.The convergence of the algorithm is proved.Numerical experiments illustrate that the proposed algorithm has higher accuracy and better image restoration quality compared with the existing randomized extended Kaczmarz(REK)method.展开更多
超大规模多输入多输出(Extra-Large Scale Multiple-Input Multiple-Output,XL-MIMO)是未来的第六代移动通信(The 6th Generation Mobile Communication Technology,6G)关键技术之一,但是由于XL-MIMO系统采用了超大规模天线阵列,其信号...超大规模多输入多输出(Extra-Large Scale Multiple-Input Multiple-Output,XL-MIMO)是未来的第六代移动通信(The 6th Generation Mobile Communication Technology,6G)关键技术之一,但是由于XL-MIMO系统采用了超大规模天线阵列,其信号处理需求非常庞大,增加了计算复杂度。这对信号的检测算法有了更高的要求,由此对XL-MIMO系统中低复杂度算法进行研究是十分重要的。首先介绍了XL-MIMO系统信道模型,然后引入了预编码技术,将随机Kaczmarz算法和传统的MMSE算法在完美非平稳信道的归一化传输功率的误码率情况、用户数量复杂度情况、天线数量复杂度情况进行了仿真分析与比较。结果表明随机Kaczmarz算法具有更低的计算复杂度,并且是一种可以准确实现的快速算法。展开更多
The Kaczmarz algorithm is a common iterative method for solving linear systems.As an effective variant of Kaczmarz algorithm,the greedy Kaczmarz algorithm utilizes the greedy selection strategy.The two-subspace projec...The Kaczmarz algorithm is a common iterative method for solving linear systems.As an effective variant of Kaczmarz algorithm,the greedy Kaczmarz algorithm utilizes the greedy selection strategy.The two-subspace projection method performs an optimal intermediate projection in each iteration.In this paper,we introduce a new greedy Kaczmarz method,which give full play to the advantages of the two improved Kaczmarz algorithms,so that the generated iterative sequence can exponentially converge to the optimal solution.The theoretical analysis reveals that our algorithm has a smaller convergence factor than the greedy Kaczmarz method.Experimental results confirm that our new algorithm is more effective than the greedy Kaczmarz method for coherent systems and the two-subspace projection method for appropriate scale systems.展开更多
基金National Natural Science Foundation of China(No.61171179,No.61171178)Natural Science Foundation of Shanxi Province(No.2010011002-1,No.2010011002-2and No.2012021011-2)
文摘The order of the projection in the algebraic reconstruction technique(ART)method has great influence on the rate of the convergence.Although many scholars have studied the order of the projection,few theoretical proofs are given.Thomas Strohmer and Roman Vershynin introduced a randomized version of the Kaczmarz method for consistent,and over-determined linear systems and proved whose rate does not depend on the number of equations in the systems in 2009.In this paper,we apply this method to computed tomography(CT)image reconstruction and compared images generated by the sequential Kaczmarz method and the randomized Kaczmarz method.Experiments demonstrates the feasibility of the randomized Kaczmarz algorithm in CT image reconstruction and its exponential curve convergence.
基金supported by the National Natural Science Foundations of China(Nos.11571171,62073161,and 61473148)。
文摘Tikhonov regularization is a powerful tool for solving linear discrete ill-posed problems.However,effective methods for dealing with large-scale ill-posed problems are still lacking.The Kaczmarz method is an effective iterative projection algorithm for solving large linear equations due to its simplicity.We propose a regularized randomized extended Kaczmarz(RREK)algorithm for solving large discrete ill-posed problems via combining the Tikhonov regularization and the randomized Kaczmarz method.The convergence of the algorithm is proved.Numerical experiments illustrate that the proposed algorithm has higher accuracy and better image restoration quality compared with the existing randomized extended Kaczmarz(REK)method.
文摘超大规模多输入多输出(Extra-Large Scale Multiple-Input Multiple-Output,XL-MIMO)是未来的第六代移动通信(The 6th Generation Mobile Communication Technology,6G)关键技术之一,但是由于XL-MIMO系统采用了超大规模天线阵列,其信号处理需求非常庞大,增加了计算复杂度。这对信号的检测算法有了更高的要求,由此对XL-MIMO系统中低复杂度算法进行研究是十分重要的。首先介绍了XL-MIMO系统信道模型,然后引入了预编码技术,将随机Kaczmarz算法和传统的MMSE算法在完美非平稳信道的归一化传输功率的误码率情况、用户数量复杂度情况、天线数量复杂度情况进行了仿真分析与比较。结果表明随机Kaczmarz算法具有更低的计算复杂度,并且是一种可以准确实现的快速算法。
基金supported by the National Natural Science Foundation of China(No.11771193).
文摘The Kaczmarz algorithm is a common iterative method for solving linear systems.As an effective variant of Kaczmarz algorithm,the greedy Kaczmarz algorithm utilizes the greedy selection strategy.The two-subspace projection method performs an optimal intermediate projection in each iteration.In this paper,we introduce a new greedy Kaczmarz method,which give full play to the advantages of the two improved Kaczmarz algorithms,so that the generated iterative sequence can exponentially converge to the optimal solution.The theoretical analysis reveals that our algorithm has a smaller convergence factor than the greedy Kaczmarz method.Experimental results confirm that our new algorithm is more effective than the greedy Kaczmarz method for coherent systems and the two-subspace projection method for appropriate scale systems.
