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New variant of the HSS iteration method for weighted Toeplitz regularized least-squares problems from image restoration

机译:HSS迭代方法的新变种,用于加权Toeplitz图像复原中的正则化最小二乘问题

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For fast solving weighted Toeplitz least-squares problems from image restoration, Ng and Pan (2014) studied a new Hermitian and skew-Hermitian splitting (NHSS) preconditioner. In this paper, a generalization of the NHSS preconditioner and the corresponding iterative method are presented. Convergence for the new iteration method is studied and optimal choice of the parameters is discussed. Bounds on the eigenvalues and the corresponding eigenvector distributions are proposed. The degree of the minimal polynomial of the preconditioned matrix is obtained. Numerical experiments arising from image restoration are provided, which show the proposed iteration method is effective and confirm our theoretical results are correct. (C) 2017 Elsevier Ltd. All rights reserved.
机译:为了从图像恢复中快速解决加权Toeplitz最小二乘问题,Ng和Pan(2014)研究了一种新的Hermitian和Skew-Hermitian分裂(NHSS)预处理器。本文介绍了NHSS预处理器的推广和相应的迭代方法。研究了新迭代方法的收敛性,并讨论了参数的最佳选择。提出了特征值的界和相应的特征向量分布。获得预处理矩阵的最小多项式的程度。提供了图像复原的数值实验,表明所提出的迭代方法是有效的,并证明了我们的理论结果是正确的。 (C)2017 Elsevier Ltd.保留所有权利。

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