"Summary: the quest for a general functional tensor framework for blind source separationOur overall objective is the development of a general functional framework for solving tensor based blind source separation (BSS) problems in biomedical data fusion, using tensor decompositions (TDs) as basic core. We claim that TDs will allow the extraction of fairly complicated sources of biomedical activity from fairly complicated sets of uni- and multimodal data. The power of the new techniques will be demonstrated for three well-chosen representative biomedical applications for which extensive expertise and fully validated datasets are available in the PI’s team, namely:• Metabolite quantification and brain tumour tissue typing using Magnetic Resonance Spectroscopic Imaging,• Functional monitoring including seizure detection and polysomnography,• Cognitive brain functioning and seizure zone localization using simultaneous Electroencephalography-functional MR Imaging integration.Solving these challenging problems requires that algorithmic progress is made in several directions:• Algorithms need to be based on multilinear extensions of numerical linear algebra.• New grounds for separation, such as representability in a given function class, need to be explored.• Prior knowledge needs to be exploited via appropriate health relevant constraints.• Biomedical data fusion requires the combination of TDs, coupled via relevant constraints.• Algorithms for TD updating are important for continuous long-term patient monitoring.The algorithms are eventually integrated in an easy-to-use open source software platform that is general enough for use in other BSS applications.Having been involved in biomedical signal processing over a period of 20 years, the PI has a good overview of the field and the opportunities. By working directly at the forefront in close collaboration with the clinical scientists who actually use our software, we can have a huge impact."