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<p>In this paper, we first develop an algorithm for computing the singular value decomposition (SVD) of a third-order reduced biquaternion tensor via a new Ht-product. As theoretical applications, the Moore-Penrose inverse of a third-order reduced biquaternion tensor is defined and its characterizations are discussed via its SVD. Using the Moore-Penrose inverses, we mainly discuss the general (or Hermitian) solutions to reduced biquaternion tensor equation <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {A}*\mathcal {X}=\mathcal {B}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">A</mi> <mrow /> <mo>∗</mo> <mi mathvariant="script">X</mi> <mo>=</mo> <mi mathvariant="script">B</mi> </mrow> </math></EquationSource> </InlineEquation> as well as its least-squares solutions. Finally, two novel fast algorithms are developed and applied in color video compression and deblurring. Both of which perform better than the compared algorithms, especially in CPU time.</p>

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Reduced biquaternion tensors and applications in color video processing

  • 期刊论文

  • 发表日期：

    2025年12月2日

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  • Cui E Yu,
  • Xin Liu,
  • Hui Luo,
  • Yang Zhang

摘要

In this paper, we first develop an algorithm for computing the singular value decomposition (SVD) of a third-order reduced biquaternion tensor via a new Ht-product. As theoretical applications, the Moore-Penrose inverse of a third-order reduced biquaternion tensor is defined and its characterizations are discussed via its SVD. Using the Moore-Penrose inverses, we mainly discuss the general (or Hermitian) solutions to reduced biquaternion tensor equation \(\mathcal {A}*\mathcal {X}=\mathcal {B}\) A ∗ X = B as well as its least-squares solutions. Finally, two novel fast algorithms are developed and applied in color video compression and deblurring. Both of which perform better than the compared algorithms, especially in CPU time.