Properties of a general quaternion-valued gradient operator and its applications to signal processing

作     者：Meng-di JIANG Yi LI Wei LIU 

作者机构：Department of Electronic and Electrical EngineeringUniversity of Sheffield School of Mathematics and StatisticsUniversity of Sheffield 

出 版 物：《Frontiers of Information Technology & Electronic Engineering》 (信息与电子工程前沿（英文版）)

年 卷 期：2016年第17卷第2期

页      面：83-95页

核心收录：

学科分类：0808[工学-电气工程] 0809[工学-电子科学与技术（可授工学、理学学位）] 07[理学] 08[工学] 070104[理学-应用数学] 0810[工学-信息与通信工程] 0711[理学-系统科学] 0839[工学-网络空间安全] 080401[工学-精密仪器及机械] 0804[工学-仪器科学与技术] 080402[工学-测试计量技术及仪器] 0835[工学-软件工程] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：supported by the National Grid UK 

主　　题：Quaternion Gradient operator Signal processing Least mean square(LMS) algorithm Nonlinear adaptive filtering Adaptive beamforming 

摘      要：The gradients of a quaternion-valued function are often required for quaternionic signal processing *** HR gradient operator provides a viable framework and has found a number of ***,the applications so far have been limited to mainly real-valued quaternion functions and linear quaternionvalued *** generalize the operator to nonlinear quaternion functions,we define a restricted version of the HR operator,which comes in two versions,the left and the right *** then present a detailed analysis of the properties of the operators,including several different product rules and chain *** the new rules,we derive explicit expressions for the derivatives of a class of regular nonlinear quaternion-valued functions,and prove that the restricted HR gradients are consistent with the gradients in the real *** an application,the derivation of the least mean square algorithm and a nonlinear adaptive algorithm is *** results based on vector sensor arrays are presented as an example to demonstrate the effectiveness of the quaternion-valued signal model and the derived signal processing algorithm.