Model-based algorithm development with focus on biosignal processing

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In recent years, the rise of affordable and robust sensors, along with increased internet availability, has led to an unprecedented surge in data generation. This data explosion has created a heightened demand for algorithms to process it. However, a crucial yet often overlooked aspect is the need for sophisticated mathematical modeling to accompany these advanced algorithms. This thesis investigates the interplay between algorithm design and modeling, focusing on applications in biomedical engineering. The analysis of physiological time series illustrates two key challenges that underscore the significance of modeling. First, the high noise levels in biological signals necessitate strong regularization, achievable through modeling. Second, many medical applications involve latent variables that are not directly observable, requiring estimation through models. Throughout the discussion, we will explore two primary modalities: Ballistocardiography (BCG), commonly used in home monitoring with simple pressure sensors that produce scalar signals, and functional magnetic resonance imaging (fMRI), a complex method capable of generating detailed images of brain functionality. These examples highlight the critical relationship between data processing, algorithm development, and mathematical modeling in biomedical contexts.