Near orthogonal discrete quaternion Fourier transform components via an optimal frequency rescaling approach

Hu, Lingyue; Ling, Bingo Wing‐Kuen; Ho, Charlotte Yuk-Fan; Huang, Guoheng

doi:10.1049/iet-spr.2020.0199

Cited by 3 publications

(1 citation statement)

References 19 publications

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“…On the other hand, a quaternion valued number is a number having three imaginary valued components and one real valued component [14][15][16][17]. By grouping the color planes of a hyperspectral image into the groups with each group having four color planes, forming the quaternion valued matrices, applying the quaternion valued singular spectrum analysis to the quaternion valued matrices, selecting the two dimensional quaternion valued singular spectrum analysis components and reconstructing the hyperspectral image, the correlation among both the pixels within each color plane and the pixels across different color planes are exploited [18].…”

Section: Introductionmentioning

confidence: 99%

Hyperspectral Image Enhancement by Two Dimensional Quaternion Valued Singular Spectrum Analysis for Object Recognition

Lin

Ling

et al. 2021

Remote Sensing

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This paper proposes a two dimensional quaternion valued singular spectrum analysis based method for enhancing the hyperspectral image. Here, the enhancement is for performing the object recognition, but neither for improving the visual quality nor suppressing the artifacts. In particular, the two dimensional quaternion valued singular spectrum analysis components are selected in such a way that the ratio of the interclass separation to the intraclass separation of the pixel vectors is maximized. Next, the support vector machine is employed for performing the object recognition. Compared to the conventional two dimensional real valued singular spectrum analysis based method where only the pixels in a color plane is exploited, the two dimensional quaternion valued singular spectrum analysis based method fuses four color planes together for performing the enhancement. Hence, both the spatial information among the pixels in the same color plane and the spectral information among various color planes are exploited. The computer numerical simulation results show that the overall classification accuracy based on our proposed method is higher than the two dimensional real valued singular spectrum analysis based method, the three dimensional singular spectrum analysis based method, the multivariate two dimensional singular spectrum analysis based method, the median filtering based method, the principal component analysis based method, the Tucker decomposition based method and the hybrid spectral convolutional neural network (hybrid SN) based method.

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Section: Introductionmentioning

confidence: 99%

Hyperspectral Image Enhancement by Two Dimensional Quaternion Valued Singular Spectrum Analysis for Object Recognition

Lin

Ling

et al. 2021

Remote Sensing

Self Cite

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Rotated quaternion valued algebra and its application to discrete time rotated quaternion valued Fourier transform based human signal processing

Wei,

Hu,

Ling

et al. 2023

2023 IEEE International Symposium on Product Compliance Engineering - Asia (ISPCE-ASIA)

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Discrete octonion linear canonical transform associated with finite-length function

Wang,

Gao

2024

Int. J. Geom. Methods Mod. Phys.

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In this paper, the discrete octonion linear canonical transform (DOCLCT) is presented. According to the definition of DOCLCT, its shift transform and modulation transform are explored. In addition, based on a new convolution operator, we obtain the convolution theorem of DOCLCT. The DOCLCT can be derived by the three-dimensional (3D) linear canonical transform. So, the fast algorithm of 3D DOCLCT is discussed. Finally, Heisenberg’s uncertainty principle associated with DOCLCT is established.

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Near orthogonal discrete quaternion Fourier transform components via an optimal frequency rescaling approach

Cited by 3 publications

References 19 publications

Hyperspectral Image Enhancement by Two Dimensional Quaternion Valued Singular Spectrum Analysis for Object Recognition

Hyperspectral Image Enhancement by Two Dimensional Quaternion Valued Singular Spectrum Analysis for Object Recognition

Rotated quaternion valued algebra and its application to discrete time rotated quaternion valued Fourier transform based human signal processing

Discrete octonion linear canonical transform associated with finite-length function

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