Research PaperNo Access

Explicit Haar–Schauder multiwavelet filters and algorithms. Part II: Relative entropy-based estimation for optimal modeling of biomedical signals

Université de Sousse, Ecole Nationale d’Ingénieurs de Sousse, LATIS — Laboratory of Advanced Technology and Intelligent Systems, 4023, Sousse, Tunisie

E-mail Address: makeremzemni@gmail.com

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Malika Jallouli

Université de Sousse, Ecole Nationale d’Ingénieurs de Sousse, LATIS — Laboratory of Advanced Technology and Intelligent Systems, 4023, Sousse, Tunisie

E-mail Address: jallouli.malika3@gmail.com

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Anouar Ben Mabrouk

http://orcid.org/0000-0002-2571-1066

Algebra, Number Theory and Nonlinear Analysis Lab. LR18ES15, Department of Mathematics, Faculty of Sciences, University of Monastir, Monastir 5000, Tunisia

Department of Mathematics, Higher Institute of Applied Mathematics and Informatics University of Kairouan, Street of Assad Ibn Al Fourat, Kairouan 3100, Tunisia

Department of Mathematics, Faculty of Sciences, University of Tabuk, King Faisal Rd, Tabuk, Saudi Arabia

E-mail Address: anouar.benmabrouk@fsm.rnu.tn

Corresponding author.

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, and

Mohamed Ali Mahjoub

Université de Sousse, Ecole Nationale d’Ingénieurs de Sousse, LATIS — Laboratory of Advanced Technology and Intelligent Systems, 4023, Sousse, Tunisie

E-mail Address: medalimahjoub@gmail.com

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https://doi.org/10.1142/S0219691319500383Cited by:11 (Source: Crossref)

Abstract

Biomedical signal/image processing and analysis are always fascinating tasks in scientific researches, both theoretical and practical. One of the powerful tools in such topics is wavelet theory which has been proved to be challenging since its discovery. One of the best measures of the optimality of reconstruction of signals/images is the well-known Shannon’s entropy. In wavelet theory, this is very well known and researchers are familiar with it. In the present work, a step forward is proposed based on more general wavelet tools. New approach is proposed for the reconstruction of signals/images provided with multiwavelets Shannon-type entropy to evaluate the order/disorder of the reconstructed signals/images. Efficiency and accuracy of the approach is confirmed by a simulation study on several models such as ECG, EEG and DNA/Proteins’ signals.

Keywords:

AMSC: 35C55, 60G35, 76M27

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