信号处理中四元数特征值问题的迭代算法

IF 3.2 2区 工程技术 Q2 ENGINEERING, ELECTRICAL & ELECTRONIC IEEE Signal Processing Letters Pub Date : 2024-09-11 DOI:10.1109/LSP.2024.3459640
Qiankun Diao;Jinlan Liu;Naimin Zhang;Dongpo Xu
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引用次数: 0

摘要

这封信提出了一种基于广义 $\mathbb {HR}$ 微积分的四元数投影梯度上升(QPGA)迭代算法,用于计算四元数赫米矩阵的主特征值及其特征向量。我们还证明了 QPGA 算法的收敛性,证明估计的主特征值序列是单调递增的。数值实验证明了所提出的迭代法在准确性和速度方面优于传统的代数方法,并证明了 QPGA 算法得到的主特征值及其特征向量在用四元数主成分分析法去噪和用四元数最小均方(QLMS)算法过滤胎儿心电图中的应用。总之,快速四元数特征值求解方法为四元数信号处理提供了一种新颖有效的技术工具。
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An Iterative Algorithm for Quaternion Eigenvalue Problems in Signal Processing
This letter proposes a quaternion projection gradient ascent (QPGA) iterative algorithm based on generalized $\mathbb {HR}$ calculus for computing the principal eigenvalues and its eigenvectors of quaternion Hermitian matrices. We also prove the convergence of the QPGA algorithm, demonstrating that the estimated sequence of principal eigenvalues is monotonically increasing. Numerical experiments demonstrate the superiority of the proposed iterative method over traditional algebraic methods in terms of accuracy and speed, as well as the application of principal eigenvalues and their eigenvectors obtained by the QPGA algorithm in denoising with quaternion principal component analysis and quaternion least mean square (QLMS) algorithms in filtering fetal electrocardiograms. Overall, the fast quaternion eigenvalue solving method provides a novel and effective technical tool for quaternion signal processing.
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来源期刊
IEEE Signal Processing Letters
IEEE Signal Processing Letters 工程技术-工程:电子与电气
CiteScore
7.40
自引率
12.80%
发文量
339
审稿时长
2.8 months
期刊介绍: The IEEE Signal Processing Letters is a monthly, archival publication designed to provide rapid dissemination of original, cutting-edge ideas and timely, significant contributions in signal, image, speech, language and audio processing. Papers published in the Letters can be presented within one year of their appearance in signal processing conferences such as ICASSP, GlobalSIP and ICIP, and also in several workshop organized by the Signal Processing Society.
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