https://doi.org/10.1140/epjp/s13360-025-06028-2
Regular Article
A Lanczos algorithm for computing split quaternion partial singular value decomposition and its application
College of Mathematics Science, Liaocheng University, 252000, Liaocheng, Shandong, China
Received:
4
July
2024
Accepted:
15
January
2025
Published online:
7
February
2025
Partial singular value decomposition (PSVD) is often used to deal with dimensionality reduction, compression and data approximation of large matrices to improve computational efficiency and simplify the analysis of complex data. In this paper, we will study the problem of PSVD of split quaternion matrix. By analyzing the structure of the real representation matrix, we find that it can preserve the partially unitary property. Based on the property of the real representation matrix, we propose split quaternion partial singular value decomposition (SQPSVD) and Lanczos algorithm of SQPSVD. In numerical examples, we verify the effectiveness of the Lanczos algorithm and propose the split quaternion color image model to apply the Lanczos algorithm to color image processing. The combination of the model and algorithm has a good performance in low rank approximation of color images, color face reconstruction and recognition. Moreover, based on the Lanczos algorithm, we propose the denoising algorithm for the space magnetic field measurement data and the experimental result shows the effectiveness of the denoising algorithm.
This work is supported by the National Natural Science Foundation of China under grants 62176112, the Natural Science Foundation of Shandong Province under grant ZR2022MA030, and the Discipline with Strong Characteristics of Liaocheng University–Intelligent Science and Technology under grant 319462208.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
