11th December 2009 4 p.m. Building 54, room 10B
SYMBIOSIS Seminar - Non-convexly constrained inverse problems; From mathematics to biomedical imaging
Thomas Blumensath
School of Mathematics, University of Southampton
- Categories
- Inverse problems
- Submitter
- Thomas Blumensath
In many scientific areas, we are interested in phenomena that cannot be directly observed and we instead have to infer the phenomenon from related observations. Similarly, in engineering, we can often observe the response of a known system and need to determine the phenomenon driving the system. For example, in CT imaging, given a set of 2 dimensional x-ray images we would like to build up a three dimensional picture of a patient’s anatomy, or in geophysical exploration, we want to chart geological structures in the Earth’s crust given only a set of recordings of seismic reflections collected at the surface.
In many instances these inverse problems are ill posed; we are even in theory unable to make reliable inferences without the use of additional assumptions. Over the last few years, a new theory called ‘Compressed Sensing’ has emerged that revolutionises the way we think about certain inverse problems and promises to lead to substantial breakthroughs in many application areas.
In this talk I will give an overview of this emerging area at the intersection between mathematics, engineering and computer science and will show how results from areas such as convex and non-convex optimisation, high dimensional geometry, probability theory, Banach space theory and numerical analysis can be used to better understand and thus improve medical imaging systems.