Quaternion tensor low rank Quaternion tensor low-rank approximation using a family of non-convex norms

Alaeddine Zahir; Ahmed Ratnani; Khalide Jbilou

doi:10.1007/s11075-025-02226-2

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arXiv · 2409.10724

Quaternion tensor low rank Quaternion tensor low-rank approximation using a family of non-convex norms

Alaeddine Zahir·Ahmed Ratnani·Khalide Jbilou

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Abstract

In this paper, we propose a new approaches for low rank approximation of quaternion tensors \cite{chen2019low,zhang1997quaternions,hamilton1866elements}. The first method uses quasi-norms to approximate the tensor by a low-rank tensor using the QT-product \cite{miao2023quaternion}, which generalizes the known L-product to N-mode quaternions. The second method involves Non-Convex norms to approximate the Tucker and TT-rank for the completion problem. We demonstrate that the proposed methods can effectively approximate the tensor compared to the convexifying of the rank, such as the nuclear norm. We provide theoretical results and numerical experiments to show the efficiency of the proposed methods in the Inpainting and Denoising applications.

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Alaeddine Zahir, Ahmed Ratnani, Khalide Jbilou. 2024-09-16. Quaternion tensor low rank Quaternion tensor low-rank approximation using a family of non-convex norms. https://doi.org/10.1007/s11075-025-02226-2

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