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.

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Biosignals are nowadays important subjects for scientific researches from both theory, and applications, especially, with the appearance of new pandemics threatening the humanity such as the new coronavirus. One aim in the present work is to prove that wavelets may be a successful machinery to understand such phenomena by applying a step forward extension of wavelets to multi-wavelets. We proposed in a first step to improve multi-wavelet notion by constructing more general families using independent components for multi-scaling and multi-wavelet mother functions. A special multi-wavelet is then introduced, continuous, and discrete multi-wavelet transforms are associated, as well as new filters, and algorithms of decomposition, and reconstruction. Applied breakthroughs of the paper may be summarized in three aims. In a first direction, an approximation (reconstruction) of a classical (stationary, periodic) example dealing with Fourier modes has been conducted in order to confirm the efficiency of the HSch multi-wavelets in approximating such signals and in providing fast algorithms. The second experimentation is concerned with the decomposition and reconstruction application of the HSch multi-wavelet on an ECG signal. The last experimentation is concerned with a de-noising application on a strain of coronavirus signal permitting to localize approximately the transmembrane segments of such a series as neighborhoods of the local maxima of an numerized version of the strain. Accuracy of the method has been evaluated by means of error estimates and statistical tests.

No abstract

Biosignals are nowadays important subjects for scientific researches from both theory, and applications, especially, with the appearance of new pandemics threatening the humanity such as the new Coronavirus. One aim in the present work is to prove that Wavelets may be a successful machinery to understand such phenomena by applying a step forward extension of wavelets to multi-wavelets. We proposed in a first step to improve multi-wavelet notion by constructing more general families using independent components for multi-scaling, and multi-wavelet mother functions. A special multi-wavelet is then introduced, continuous, and discrete multi-wavelet transforms are associated, as well as new filters, and algorithms of decomposition, and reconstruction. The constructed multi-wavelet framework is applied for some experimentations showing fast algorithms, ECG signal, and a strain of Coronavirus processing.