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.

Department of Mathematics and Didactics of Mathematics Technical University of Liberec Studentská 2 Liberec Czech Republic

Mathematics Department Aston University Birmingham B3 7ET UK

Zobrazit více v PubMed

Andrle M., Rebollo-Neira L. Cardinal B-spline dictionaries on a compact interval. Appl. Comput. Harmon. Anal. 2005;18:336–346. doi: 10.1016/j.acha.2005.01.001. DOI

Andrle M., Rebollo-Neira L. From cardinal spline wavelet bases to highly coherent dictionaries. J. Phys. A. 2008;41(172001) doi: 10.1088/1751-8113/41/17/172001. article No. DOI

Cohen A., Daubechies I., Feauveau J.C. Biorthogonal bases of compactly supported wavelets. Commun. Pure Appl. Math. 1992;45:485–560. doi: 10.1002/cpa.3160450502. DOI

Cohen A. Elsevier; Amsterdam: 2003. Numerical Analysis of Wavelet methods, Studies in Mathematics and its Applications 32.

Chen D. Spline wavelets of small support. SIAM J. Math. Anal. 1995;26:500–517. doi: 10.1137/S0036141093245264. DOI

Chui C., Wang J. On compactly supported spline wavelets and a duality principle. Trans. Am. Math. Soc. 1992;330:903–915. doi: 10.2307/2153941. DOI

Černá D., Finěk V., Najzar K. On the exact values of coefficients of coiflets. Cent. Eur. J. Math. 2008;6:159–169. doi: 10.2478/s11533-008-0011-2. DOI

https://physionet.org/physiobank/database/mitdb/ (Last access February 2021).

http://www.nonlinear-approx.info/examples/node013.html (Last access February 2021).

Daubechies I. Orthonormal bases of compactly supported wavelets. Commun. Pure Appl. Math. 1988;41:909–996. doi: 10.1002/cpa.3160410705. DOI

Daubechies I. Orthonormal bases of compactly supported wavelets II, variations on a theme. SIAM J. Math. Anal. 1993;24:499–519. doi: 10.1137/0524031. DOI

Han B., Shen Z. Wavelets with short support. SIAM J. Math. Anal. 2006;38:530–556. doi: 10.1137/S0036141003438374. DOI

Lee S.J., Kim J., Lee M. A real-time ECG data compression and transmission algorithm for an e-health device. IEEE Trans. Biomed. Eng. 2011;58:2448–2455. doi: 10.1109/TBME.2011.2156794. PubMed DOI

Ma J.L., Zhang T.T., Dong M.C. A novel ECG data compression method using adaptive Fourier decomposition with security guarantee in e-health applications. IEEE J. Biomed. Health Inform. 2015;19:986–994. doi: 10.1109/JBHI.2014.2357841. PubMed DOI

Pandey A., Singh B., Sain S, Sood N. A joint application of optimal threshold based discrete cosine transform and ASCII encoding for ECG data compression with its inherent encryption. Australas. Phys. Eng. Sci. Med. 2016;39:833–855. doi: 10.1007/s13246-016-0476-4. PubMed DOI

Raj S., Ray K.C. Sparse representation of ECG signals for automated recognition of cardiac arrhythmias. Expert Syst. Appl. 2018;10:49–64. doi: 10.1016/j.eswa.2018.03.038. DOI

Rebollo-Neira L., Černá D. Wavelet based dictionaries for dimensionality reduction of ECG signals. Biomed. Signal Process. Control. 2019;54(101593) doi: 10.1016/j.bspc.2019.101593. article No. DOI

Rebollo-Neira L., Lowe D. Optimized orthogonal matching pursuit approach. IEEE Signal Process. Lett. 2002;9:137–140. doi: 10.1109/LSP.2002.1001652. DOI

Rebollo-Neira L. Cooperative greedy pursuit strategies for sparse signal representation by partitioning. Signal Process. 2016;125:365–375. doi: 10.1016/j.sigpro.2016.02.008. DOI

Rebollo-Neira L. Effective high compression of ECG signals at low level distortion. Sci. Rep. 2019;9(4564) doi: 10.1038/s41598-019-40350-x. article No. PubMed DOI PMC

Rebollo-Neira L., Xu Z. Sparse signal representation by adaptive non-uniform B-spline dictionaries on a compact interval. Signal Process. 2010;90:2308–2313. doi: 10.1016/j.sigpro.2010.02.004. DOI

Strang G. Wavelets and dilation equations: a brief introduction. SIAM Rev. 1989;31(4):614–627. https://www.jstor.org/stable/2031540

Williams J., Amaratunga K. Introduction to wavelets in engineering. Int. J. Numer. Methods Eng. 1994;37:2365–2388. Wiley.

Tan C., Zhang L., Wu H. A novel Blaschke unwinding adaptive Fourier decomposition based signal compression algorithm with application on ECG signals. IEEE J. Biomed. Health Inform. 2019;23:672–682. doi: 10.1109/JBHI.2018.2817192. PubMed DOI