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A two-sided randomized algorithm for low-rank quaternion matrix approximation
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DOI：10.1016/j.aml.2025.109655.png)
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Abstract
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The low-rank quaternion matrix approximation has a wide range of applications in color image inpainting, video compression, and face recognition. This paper presents a two-sided randomization (TSR-svdQ) algorithm to approximate the quaternion singular value decomposition (QSVD) via low-dimensional projections, which greatly reduces computational complexity. An upper bound for the expected approximation error of the proposed algorithm is given. Numerical examples are provided to demonstrate the effectiveness of the proposed algorithm compared with the randomized QSVD developed by Liu et al. (2022) in terms of computing time. Applied to color face recognition problems, the TSR-svdQ algorithm obtains higher recognition accuracies and behaves more efficient than the known Lanczos-based partial QSVD.
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2.8
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