Discrete cosine transform LSQR methods for multidimensional ill-posed problems

Document Type : Research Article


1 Centre for Behavioral Economics and Decision Making(CBED), FGSES, Mohammed VI Polytechnic University, Green City, Morocco

2 Laboratoire de Mathématiques, Informatique et Applications, Securite de l'Information LABMIA-SI, University Mohamed V, Rabat Morocco; University Littoral Cote d'Oplae, France

3 LMPA, 50 rue F. Buisson, ULCO Calais, France; Mohammed VI Polytechnic University, Green City, Morocco


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.