V-系统的快速变换算法  

A fast algorithm for V-system

作　　者：陈伟[1] 戚谨雯 李坚 宋瑞霞[3] CHEN Wei;QI Jinwen;LI Jian;SONG Ruixia(School of Artificial Intelligence and Computer Science,Jiangnan University,Wuxi 214122,Jiangsu Province,China;Faculty of Applied Sciences,Macao Polytechnic University,Macao 999078,China;College of Sciences,North China University of Technology,Beijing 100144,China)

机构地区：[1]江南大学人工智能与计算机学院,江苏无锡214122 [2]澳门理工大学应用科学学院,中国澳门999078 [3]北方工业大学理学院,北京100144

出　　处：《浙江大学学报（理学版）》2023年第6期761-769,共9页Journal of Zhejiang University（Science Edition）

摘　　要：V-系统是L2[0,1]上的一类完备正交分段多项式函数系,由于其基函数的间断特性,在非连续信号的表达与分析上优势显著。然而,在目前的V-系统变换算法中,对于一个长度为N的信号,不仅需要事先生成并存储一个N阶的正交矩阵,而且其时间复杂度高达Ο(N^(3))。为实现对大规模数据的高效处理,从V-系统的多分辨率分析角度出发,设计并实现了V-系统的快速分解与重构算法,不仅无须存储额外信息,而且其时间复杂度仅为Ο(N)。测试结果表明,提出的快速算法能够满足大规模数据高效处理要求,为V-系统在更多领域的应用奠定了基础。V-system is a kind of complete orthogonal piecewise polynomial function system on L2[0,1],because of the discontinuous nature of its basis functions,it has significant advantages in the expression and analysis of discontinuous signals.However,in the current V-system transformation algorithm,for a signal with a length of N,it not only needs to generate and store an N-order orthogonal matrix in advance,but also its time complexity is as high asΟ(N^(3)).Therefore,in order to adapt to the efficient processing needs,this paper designs and implements a fast decomposition and reconstruction algorithm for V-systems from the perspective of multi-resolution analysis of V-systems.This fast algorithm does not need to store additional information,and its time complexity is onlyΟ(N^(2)).The test results show that the fast algorithm proposed in this paper can meet the requirements of high-efficiency processing of large-scale data,which lays the foundation for the application of V-system in more fields.

关 键 词：V-系统 多分辨率分析 双尺度方程 多小波 快速算法 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]