On tensor GMRES and Golub-Kahan methods via the T-product for color image processing

IF 0.7 4区 数学 Q2 Mathematics
M. E. Guide, Alaa El Ichi, K. Jbilou, R. Sadaka
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引用次数: 20

Abstract

The present paper is concerned with developing tensor iterative Krylov subspace methods to solve large multi-linear tensor equations. We use the T-product for two tensors to define tensor tubal global Arnoldi and tensor tubal global Golub-Kahan bidiagonalization algorithms. Furthermore, we illustrate how tensor-based global approaches can be exploited to solve ill-posed problems arising from recovering blurry multichannel (color) images and videos, using the so-called Tikhonov regularization technique, to provide computable approximate regularized solutions. We also review a generalized cross-validation and discrepancy principle type of criterion for the selection of the regularization parameter in the Tikhonov regularization. Applications to image sequence processing are given to demonstrate the efficiency of the algorithms.
利用t积对张量GMRES和Golub-Kahan方法进行彩色图像处理
本文研究了求解大型多线性张量方程的张量迭代Krylov子空间方法。我们利用两个张量的t积定义了张量管全局Arnoldi和张量管全局Golub-Kahan双对角化算法。此外,我们说明了如何利用基于张量的全局方法来解决由恢复模糊的多通道(彩色)图像和视频引起的不适定问题,使用所谓的Tikhonov正则化技术,以提供可计算的近似正则化解决方案。我们还回顾了在Tikhonov正则化中选择正则化参数的广义交叉验证和差异原则类型的准则。最后给出了该算法在图像序列处理中的应用。
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来源期刊
CiteScore
1.20
自引率
14.30%
发文量
45
审稿时长
6-12 weeks
期刊介绍: The journal is essentially unlimited by size. Therefore, we have no restrictions on length of articles. Articles are submitted electronically. Refereeing of articles is conventional and of high standards. Posting of articles is immediate following acceptance, processing and final production approval.
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