Open AccessOn tensor GMRES and Golub-Kahan methods via the T-product for color image processing
Author(s) -
M. El Guide,
Alaa El Ichi,
Khalide Jbilou,
Rachid Sadaka
Publication year - 2021
Publication title -
the electronic journal of linear algebra
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.447
H-Index - 31
eISSN - 1537-9582
pISSN - 1081-3810
DOI - 10.13001/ela.2021.5471
Subject(s) - tikhonov regularization , mathematics , krylov subspace , generalized minimal residual method , tensor product , regularization (linguistics) , tensor (intrinsic definition) , mathematical optimization , iterative method , algorithm , inverse problem , mathematical analysis , computer science , artificial intelligence , pure mathematics
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.