Towards New Multiwavelets: Associated Filters and Algorithms. Part I: Theoretical Framework and Investigation of Biomedical Signals, ECG and Coronavirus Cases
This work addresses the need for improved signal processing tools in biomedical applications, such as ECG analysis and pandemic monitoring, but appears incremental as it builds on existing multiwavelet concepts.
The authors tackled the problem of analyzing biomedical signals like ECG and Coronavirus data by extending wavelets to multiwavelets, proposing a new theoretical framework with independent components for multi-scaling and multiwavelet functions, and applied it to show fast algorithms for signal processing.
Biosignals are nowadays important subjects for scientific researches from both theory and applications especially with the appearance of new pandemics threatening humanity such as the new Coronavirus. One aim in the present work is to prove that Wavelets may be successful machinery to understand such phenomena by applying a step forward extension of wavelets to multiwavelets. We proposed in a first step to improve the multiwavelet notion by constructing more general families using independent components for multi-scaling and multiwavelet mother functions. A special multiwavelet is then introduced, continuous and discrete multiwavelet transforms are associated, as well as new filters and algorithms of decomposition and reconstruction. The constructed multiwavelet framework is applied for some experimentations showing fast algorithms, ECG signal, and a strain of Coronavirus processing.