On tensor gmres and golub-kahan methods via the t-product for color image processing∗

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Output type: Journal article

UM6P affiliated Publication?: Yes

Author list: El Guide M., El Ichi A., Jbilou K., Sadaka R.


Publication year: 2021

Volume number: 37

Start page: 524

End page: 543

Number of pages: 20

ISSN: 1537-9582

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85111703916&doi=10.13001%2fela.2021.5471&partnerID=40&md5=573dfe51a63614447bd086c3473513f4

Languages: English (EN-GB)

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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. © 2021, International Linear Algebra Society. All rights reserved.


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Last updated on 2021-21-11 at 23:16