Generalized sampling expansions associated with quaternion Fourier transform

Dong, Cheng; Kou, Kit Ian

doi:10.1002/mma.4423

Cited by 19 publications

(4 citation statements)

References 47 publications

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“…Generalized sampling expansions associated with quaternion Fourier transform are developed in [33]. A motivation is that quaternion-valued signals along with the quaternion Fourier transform [97,99,106] provide an effective framework for vector-valued signal and image processing.…”

Section: Quaternionic Signal Processingmentioning

confidence: 99%

New Applications of Clifford’s Geometric Algebra

Breuils

Tachibana

Hitzer

2022

Adv. Appl. Clifford Algebras

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The new applications of Clifford's geometric algebra surveyed in this paper include kinematics and robotics, computer graphics and animation, neural networks and pattern recognition, signal and image processing, applications of versors and orthogonal transformations, spinors and matrices, applied geometric calculus, physics, geometric algebra software and implementations, applications to discrete mathematics and topology, geometry and geographic information systems, encryption, and the representation of higher order curves and surfaces.

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Section: Quaternionic Signal Processingmentioning

confidence: 99%

New Applications of Clifford’s Geometric Algebra

Breuils

Tachibana

Hitzer

2022

Adv. Appl. Clifford Algebras

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“…A quaternion matrix is a generalization of a complex matrix in quaternion algebra. By now, quaternions and quaternion matrices have a wide range of applications in signal processing [2][3][4], machine learning [5,6], and particularly in color image processing [7][8][9][10][11]. By encoding the red, green, and blue channel pixel values of a color image on the three imaginary parts of quaternion matrices, this method perfectly fits the color image structure and effectively preserves the inter-relationship between the color channels [12].…”

Section: Introductionmentioning

confidence: 99%

Efficient quaternion CUR method for low-rank approximation to quaternion matrix

Wu,

Kou,

Cai

et al. 2024

Preprint

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The low-rank quaternion matrix approximation has been successfully applied in many applications involving signal processing and color image processing. However, the cost of quaternion models for generating low-rank quaternion matrix approximation is sometimes considerable due to the computation of the quaternion singular value decomposition (QSVD), which limits their application to real large-scale data. To address this deficiency, an efficient quaternion matrix CUR (QMCUR) method for low-rank approximation is suggested , which provides significant acceleration in color image processing. We first explore the QMCUR approximation method, which uses actual columns and rows of the given quaternion matrix, instead of the costly QSVD. Additionally, two different sampling strategies are used to sample the above-selected columns and rows. Then, the perturbation analysis is performed on the QMCUR approximation of noisy versions of low-rank quater-nion matrices. Extensive experiments on both synthetic and real data further reveal the superiority of the proposed algorithm compared with other algorithms for getting low-rank approximation, in terms of both efficiency and accuracy.

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“…Over the last few years, there has been a growing interest in establishing the various properties of quaternion-valued FTs, including duality, sampling, product, convolution and correlation, uncertainty principle, etc. [10][11][12][13][14][15][16]. Furthermore, QFT has been generalized to quaternion fractional Fourier and quaternion linear canonical domains [17][18][19][20][21][22], and their associated localized transforms have been investigated in [23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Convolution, Correlation, and Uncertainty Principles for the Quaternion Offset Linear Canonical Transform

Urynbassarova

Teali

2023

Mathematics

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Quaternion Fourier transform (QFT) has gained significant attention in recent years due to its effectiveness in analyzing multi-dimensional signals and images. This article introduces two-dimensional (2D) right-sided quaternion offset linear canonical transform (QOLCT), which is the most general form of QFT with additional free parameters. We explore the properties of 2D right-sided QOLCT, including inversion and Parseval formulas, besides its relationship with other transforms. We also examine the convolution and correlation theorems of 2D right-sided QOLCT, followed by several uncertainty principles. Additionally, we present an illustrative example of the proposed transform, demonstrating its graphical representation of a given signal and its transformed signal. Finally, we demonstrate an application of QOLCT, where it can be utilized to generalize the treatment of swept-frequency filters.

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Generalized sampling expansions associated with quaternion Fourier transform

Cited by 19 publications

References 47 publications

New Applications of Clifford’s Geometric Algebra

New Applications of Clifford’s Geometric Algebra

Efficient quaternion CUR method for low-rank approximation to quaternion matrix

Convolution, Correlation, and Uncertainty Principles for the Quaternion Offset Linear Canonical Transform

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