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Quaternion Matrix Singular Value Decomposition and Its Application

Author: ChenMingGang
Tutor: YanLieYa
School: Xi'an University of Architecture and Technology
Course: Applied Mathematics
Keywords: Quaternion matrix Singular Value Decomposition Dual- diagonal matrix Color image reconstruction Color image denoising
CLC: O151.23
Type: Master's thesis
Year: 2009
Downloads: 263
Quote: 1
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Abstract


Quaternion in 1843 by the British mathematician Hamilton first discovered . Quaternion finding is a major event in the history of mathematics . Quaternion algebra , geometry , physics, engineering and technology has a broad and important applications. Especially in recent years , quaternions in computer science , engineering and technology in more and more applications , more attention has been paid . Matrix factorization is an important element of matrix theory . Matrix singular value decomposition of matrix theory and matrix is not only the most basic and important calculation one of the tools , but also in control theory , system identification , signal processing, optimization problems , eigenvalue problems , least squares problems and statistics , etc. aspects of direct and important applications. This paper discusses the quaternion matrix singular value decomposition algorithm and its application . On the one hand , by means of the complex quaternion matrices , said Friends of use quaternion vector nature constructively proved quaternion matrix singular value decomposition theorem , on this basis, to achieve a quaternion matrix singular value decomposition algorithms. On the other hand , the paper by means of a complex matrix of Householder transform complex quaternion matrix representation matrix reduces to double diagonal matrix , then Householder transformation reduction of double diagonal matrix singular value decomposition, the quaternion singular value decomposition singular value in quaternion matrix and complex matrix structure expressed the sense of the relationship between left and right singular vectors constructed given quaternion matrix singular value decomposition of another algorithm . In the application, this paper introduces the quaternion matrix color image model discussed quaternion matrix singular value decomposition and the characteristics of the color image , color image reconstruction and color image denoising and other issues. In the color image denoising effects , the paper proposes a block quaternion matrix singular value decomposition method , making denoised image SNR improved. This paper presents an algorithm for the numerical examples are given , and, in Matlab7.0 programming environment , the use of these algorithms are programmed , these algorithms and procedures applied to color image processing , and that this further confirms this given quaternion matrix singular value decomposition algorithm is feasible and effective.

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Theory of algebraic equations,linear algebra > Linear Algebra > Multi - linear algebra
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