University of Guilan Journal of Mathematical Modeling 2345-394X 10 1 2022 01 01 Discrete cosine transform LSQR methods for multidimensional ill-posed problems 21 37 4817 10.22124/jmm.2021.19303.1659 EN Mohamed El Guide Centre for Behavioral Economics and Decision Making(CBED), FGSES, Mohammed VI Polytechnic University, Green City, Morocco Alaa El Ichi Laboratoire de Mathématiques, Informatique et Applications, Securite de l'Information LABMIA-SI, University Mohamed V, Rabat Morocco; University Littoral Cote d'Oplae, France Khalide Jbilou LMPA, 50 rue F. Buisson, ULCO Calais, France; Mohammed VI Polytechnic University, Green City, Morocco Journal Article 2021 04 07 We propose new tensor Krylov subspace methods  for ill-posed linear tensor problems such as color or video image restoration. Those methods are based on the tensor-tensor discrete cosine transform that gives fast tensor-tensor product computations. In particular, we will focus on the tensor discrete cosine versions of GMRES, Golub-Kahan bidiagonalisation and LSQR methods. The presented numerical tests show that the methods are very fast and give good accuracies when solving some linear tensor ill-posed problems. https://jmm.guilan.ac.ir/article_4817_85dd931b01c788d42aa9bbb266512191.pdf