Volume 63, pp. 231-246, 2025.

A Riemannian conjugate gradient method for solving the tensor fixed-rank least-squares problem

Chun-Mei Li, Yu-Ying Gu, Xue-Feng Duan, and Hui-Yan Peng

Abstract

In this paper, we consider the tensor fixed-rank least-squares problem arising in image restoration. The Riemannian conjugate gradient method with an exact line search technique is designed to solve this problem. A convergence analysis of this method is given. Numerical experiments with synthetic data and real images demonstrate the feasibility and effectiveness of the new method.

Full Text (PDF) [1.4 MB], BibTeX , DOI: 10.1553/etna_vol63s231

Key words

tensor least-squares problem, fixed-rank constraint, Riemannian conjugate gradient method, exact line search, convergence analysis

AMS subject classifications

15A69, 58C05, 65F10

Links to the cited ETNA articles

[3]	Vol. 55 (2022), pp. 92-111 Abdeslem H. Bentbib, Asmaa Khouia, and Hassane Sadok: The LSQR method for solving tensor least-squares problems