Frequently encountered problems in signal processing, such as compression, filtering/smoothing, system identification, and parameter estimation, are closely tied to the fields of approximation theory and optimization. The first step towards solving these problems involves breaking them down into smaller, more manageable subtasks. In recent years, my research has focused on developing numerical methods that simplify the problem by approximating the signals being processed through a linear combination of a finite number of elementary functions.

Rather than imposing a fixed function system, it is recommended to choose functions that include free parameters. These adaptive transformation methods allow for selecting free parameters based on the specific application. Mathematically, this involves solving a separable nonlinear least squares problem to determine the optimal values of the free parameters.

Data-driven machine learning serves as an alternative to pure model-based signal processing. Artificial deep neural networks, for instance, employ interconnected artificial neurons organized in layers. Nonetheless, the interpretability of deep learning approaches poses many challenges, as they can be seen as data-driven black box models. This is an important limitation, especially in real-world applications which reuqires interpretable and reasonable decision making, such as medical sciences and autonomous driving. Model-driven learning is an emerging branch of Explainable AI (XAI) research which addresses this issue. My ongoing research is centered around this topic, specifically the development of variable projection networks (VPNet). VPNet is a novel model-driven neural network construction that effectively combines the strengths of a mathematical model-based approaches with data-driven artificial neural networks.

In the field of applied sciences, my research focuses on interdisciplinary informatics, which necessitates not only IT and mathematical knowledge but also application-specific expertise. This frequently involves collaborating with specialists from various fields, including medical doctors, engineers, and physicists.