The Minimum-Norm Least Squares Solutions to Quaternion Tensor Systems

Xie, Mengyan; Wang, Qingwen; Zhang, Yang

doi:10.3390/sym14071460

Cited by 7 publications

(2 citation statements)

References 31 publications

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“…In order to speed up the calculation, the level set functions are updated using elementary arithmetic operations [8]. Because the suggested method views the binary image as partitions, it produces a binary tree with fewer levels and a smaller number of final clusters [9][10][11]. At last, a colour map is built with a limited colour scheme that helps keep everything looking straight.…”

Section: Introductionmentioning

confidence: 99%

A Novel Approach for Quaternion Algebra Based JSEG Color Texture Segmentation

Tripathi

Srivastava

Tiwari³

2023

IJRITCC

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In this work, a novel colour quantization approach has been applied to the JSEG colour texture segmentation using quaternion algebra. As a rule, the fundamental vectors of the colour space are derived by inverting the three RGB colour directions in the complex hyperplanes. In the proposed system, colour is represented as a quaternion because quaternion algebra provides a very intuitive means of working with homogeneous coordinates. This representation views a colour pixel as a point in the three-dimensional space. A novel quantization approach that makes use of projective geometry and level set methods has been produced as a consequence of the suggested model. The JSEG colour texture segmentation will use this technique. The new colour quantization approach utilises the binary quaternion moment preserving thresholding methodology, and is therefore a splintering clustering method. This method is used to segment the colour clusters found inside the RGB cube and the colour consistency throughout the spectrum and in the space are both considered. The results of the segmentation are compared with JSEG as well as with the most recent standard segmentation techniques. These comparisons show that the suggested quantization technique makes JSEG segmentation more robust.

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Section: Introductionmentioning

confidence: 99%

A Novel Approach for Quaternion Algebra Based JSEG Color Texture Segmentation

Tripathi

Srivastava

Tiwari³

2023

IJRITCC

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“…Some applications of color image, such as color image restoration, are closely related to the solution of quaternion linear system. Therefore, the research on the solution of quaternion linear system is also very important; Jia and Michael 20 developed the quaternion generalized minimal residual method for solving quaternion linear systems; Wang et al 21 and Xie et al 22 investigated the minimal norm least squares solution to a quaternion tensor system by using the Moore–Penrose inverses of block tensor. Using the ranks and Moore–Penrose inverses of matrices, Wang et al, 23 Xu et al, 24 and Liu et al 25 established some necessary and sufficient solvability conditions for a system of quaternion Sylvester matrix equations, respectively; Tao et al 26 derived a preconditioned modified conjugate residual method based on the Kronecker product approximations for solving quaternion tensor equations.…”

Section: Introductionmentioning

confidence: 99%

Semi‐tensor product of quaternion matrices and its application

Fan

Ding

et al. 2022

Math Methods in App Sciences

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Unlike real or complex numbers, quaternion multiplication does not satisfy the commutative law. This makes it impossible to generalize some conclusions on semi‐tensor product to quaternion directly, which is valid on real or complex number fields. In this paper, we define semi‐tensor product of quaternion matrices and study the properties of semi‐tensor product of quaternion matrices, and the conclusion is applied to the color digital image restoration model.

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Compact formula for skew-symmetric system of matrix equations

Rehman

Kyrchei

2023

Arab. J. Math.

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In this paper, we consider skew-Hermitian solution of coupled generalized Sylvester matrix equations encompassing $$*$$ ∗ -hermicity over complex field. The compact formula of the general solution of this system is presented in terms of generalized inverses when some necessary and sufficient conditions are fulfilled. An algorithm and a numerical example are provided to validate our findings. A numerical example is carried out using determinantal representations of the Moore–Penrose inverse.

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The Minimum-Norm Least Squares Solutions to Quaternion Tensor Systems

Cited by 7 publications

References 31 publications

A Novel Approach for Quaternion Algebra Based JSEG Color Texture Segmentation

A Novel Approach for Quaternion Algebra Based JSEG Color Texture Segmentation

Semi‐tensor product of quaternion matrices and its application

Compact formula for skew-symmetric system of matrix equations

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