Černá Dana, Rebollo-Neira Laura
Department of Mathematics and Didactics of Mathematics, Technical University of Liberec, Studentská 2, Liberec, Czech Republic.
Mathematics Department, Aston University, Birmingham B3 7ET, UK.
MethodsX. 2021 Mar 23;8:101314. doi: 10.1016/j.mex.2021.101314. eCollection 2021.
Technical details, algorithms, and MATLAB implementation for a method advanced in the paper ``Wavelet Based Dictionaries for Dimensionality Reduction of ECG Signals'', are presented. This work aims to be the companion of that publication, in which an adaptive mathematical model for a given ECG record is proposed. The method comprises the following building blocks.(i)Construction of a suitable redundant set, called 'dictionary', for decomposing an ECG signal as a superposition of elementary components, called 'atoms', selected from that dictionary.(ii)Implementation of the greedy strategy Optimized Orthogonal Matching Pursuit (OOMP) for selecting the atoms intervening in the signal decomposition.This paper gives the details of the algorithms for implementing stage (i), which is not fully elaborated in the previous publication. The proposed dictionaries are constructed from known wavelet families, but translating the prototypes with a shorter step than that corresponding to a wavelet basis. Stage (ii) is readily implementable by the available function OOMP.•The use of the software and the power of the technique is illustrated by reducing the dimensionality of ECG records taken from the MIT-BIH Arrhythmia Database.•The MATLAB software has been made publicly available on a dedicated website.•We provide the explanations, algorithms and software for the construction of scaling functions and wavelet prototypes for 17 different wavelet families. The procedure is designed to allow for straightforward extension of the software by the inclusion of additional options for the wavelet families.
本文介绍了论文《基于小波的字典用于心电图信号降维》中提出的一种方法的技术细节、算法及MATLAB实现。这项工作旨在作为该出版物的补充，其中提出了针对给定心电图记录的自适应数学模型。该方法包括以下几个组成部分：(i)构建一个合适的冗余集，称为“字典”，用于将心电图信号分解为从该字典中选取的基本成分（称为“原子”）的叠加；(ii)实施贪婪策略优化正交匹配追踪(OOMP)以选择参与信号分解的原子。本文给出了实现阶段(i)的算法细节，这在之前的出版物中并未充分阐述。所提出的字典由已知的小波族构建而成，但平移原型的步长比对应小波基的步长更短。阶段(ii)可通过可用函数OOMP轻松实现。•通过降低取自MIT-BIH心律失常数据库的心电图记录的维度，说明了该软件的使用和该技术的功效。•MATLAB软件已在一个专用网站上公开提供。•我们提供了用于构建17种不同小波族的尺度函数和小波原型的解释、算法及软件。该程序旨在通过为小波族包含额外选项来允许对软件进行直接扩展。
