Pulse-shaped signals require a tool that can accurately analyse and identify the peak characteristics in the spectrum. One recently developed tool available to analyse non-stationary pulse-shaped waveforms with a suitable peak reconstruction is semiclassical signal analysis (SCSA). SCSA is a signal representation method that decomposes a real positive signal y(t) into a set of squared eigenfunctions through the discrete spectrum of the Schr¨odinger operator. In this study, we apply SCSA in two directions. First, we propose a new signal denoising method based on the signal curvature. We use this technique to show that denoising the pulse-shaped signal by regularizing its curvature can yield better peak-preserving performance than traditional filters, such as moving average filter or wavelet. Second, we apply SCSA to biomedical signal analysis. The localization abilities of L2 normalized squared eigenfunctions are used in blood pressure (BP) estimation. Based on existing properties, the systolic and diastolic phases are separated into photoplethysmograms (PPGs), which are then used as features for BP estimation. In addition, the Multiparameter Intelligent Monitoring in Intensive Care (MIMIC II) database is used to test the application with more than 8000 subjects. Another application uses SCSA features to characterize EEG and MEG signals, leading to more accurate epileptic spike detection and diagnosis in epileptic patients. Both applications are validated using real datasets, which guarantees statistical reliability and motivates future work of this model in clinical applications and equipment designs.

Human health is monitored through several physiological measurements such as heart rate, blood pressure, brain activity, etc. These measurements are taken at predefined points in the body and recorded as temporal signals or colorful images for diagnosis purposes. During the diagnosis, physicians analyze these recordings, sometimes visually, to make treatment decisions. These recordings are usually contaminated with noise caused by different factors such as physiological artifacts or electronic noises of the used electrodes/instruments. Therefore, the pre-processing of these signals and images becomes a crucial need to provide clinicians with useful information to make the right decisions. This Ph.D. work proposes and discusses different biomedical signal processing algorithms and their applications. It develops novel signal/image pre-processing algorithms, based on the Semi-Classical Signal Analysis method (SCSA), to enhance the quality of biomedical signals and images. The SCSA method is based on the decomposition of the input signal or image, using the squared eigenfunctions of a Semi-Classical Schrodinger operator. This approach shows great potential in denoising, and residual water-peak suppression for Magnetic Resonance Spectroscopy (MRS) signals compared to the existing methods. In addition, it shows very promising noise removal, particularly from pulse-shaped signals and from Magnetic Resonance (MR) images. In clinical practice, extracting informative characteristics or features from these pre-processed recordings is very important for advanced analysis and diagnosis. Therefore, new features and proposed are extracted based on the SCSA and fed to machine learning models for smart biomedical diagnosis such as predicting epileptic spikes in Magnetoencephalography (MEG). Moreover, a new Quantization-based Position Weight Matrix (QuPWM) feature extraction method is proposed for other biomedical classifications, such as predicting true Poly(A) regions in a DNA sequence, multiple hand gesture prediction. These features can be used to understand different complex systems, such as hand gesture/motion mechanism and help in the smart decision-making process. Finally, combining such features with reinforcement learning models will undoubtedly help automate the diagnoses and enhance the decision-making, which will accelerate the digitization of different industrial sectors. For instance, these features can help to study and understand fish growth in an End-To-End system for aquaculture environments. Precisely, this application’s preliminary results show very encouraging insights in optimally controlling the feeding while preserving the desired growth profile.