Discrete cosine transform LSQR and GMRES methods for multidimensional ill-posed problems

2021/03/22 by M. El Guide, Guide, M. El, Alaa El Ichi +3
Engineering · Mathematics · Physics and Astronomy · #65F10 #65F22 #Electromagnetic Scattering and Analysis #FOS: Mathematics #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2103.11847

openalex publication_date 2021/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present work, we propose new tensor Krylov subspace method for ill posed linear tensor problems such as in 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.

Citations

• Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter
• Tensor Decompositions and Applications
• Analysis of Discrete Ill-Posed Problems by Means of the L-Curve
• Factorization strategies for third-order tensors

Related

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• A Fast Algorithm for Cosine Transform Based Tensor Singular Value Decomposition
• On the Golub--Kahan bidiagonalization for ill-posed tensor equations with applications to color image restoration