Mathematical foundations (R1)
The mathematical foundations of the Flagship are focused on analysing nonlinear phenomena within imaging. Often these phenomena can be best understood by using geometric techniques. For instance, probing a body with waves allows for the measurement of the travel times between points on the surface of the body. These travel times correspond to distances in a non-Euclidean space, and recovering the wave speed inside the body is equivalent to finding the geometry of the space.
Computational imaging and modelling (R2)
The research program is focused on designing efficient computational imaging algorithms based on advanced mathematical foundations and considering the requirements of experimental systems. The aim is to introduce novel high-performance imaging algorithms that take advantage of both the theoretical properties and most accurate models for the considered imaging modalities. Moreover, the algorithms should efficiently account for the prior and expert information on the imaged object and be robust to modelling errors and other uncertainties.
Uncertainty quantification and machine learning (R3)
Understanding the role of information is key to successful computational imaging. All mathematical models and data contain uncertainties, but how do they propagate to the corresponding solutions? Moreover, how can imaging algorithms exploit the vast amounts of data available due to the explosion in data gathering over the past decade? Statistics and machine learning (ML) provide principled approaches to address these questions. Our research is motivated by the challenges of quantifying uncertainties in biomedical imaging, non-destructive testing, weather prediction, climate models, and the estimation of natural resources and energy efficiency.
Experimental system development (R4)
Our research focuses on optimizing computational approaches for efficient use of imaging devices and designing new measurement systems for industrial applications. Developing computational methodologies and instrumentation concurrently is essential to fully harness the potential of modern imaging systems. Our research not only aims for scientific breakthroughs but also seeks practical applications in industrial monitoring, control and medical diagnostics, together with our stakeholders.