Construction of wavelet dictionaries for ECG modeling

Abstract

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.