In 1976 Keller formulated the following very general definition of inverse problems, which is often cited in the literature:
"We call two problems inverses of one another if the formulation of each involves all or part of the solution of the other. Often, for historical reasons, one of the two problems has been studied extensively for some time, while the other is newer and not so well understood. In such cases, the former problem is called the direct problem, while the latter is called the inverse problem."
Inverse problems appear in many situations in physics, engineering, biology and medicine. The main mathematical problem is the well (ill) posedness of the inversion process. Indeed, in practice most inverse problems are ill-posed in terms of non-uniqueness or lack of stability of the inversion.
This one-day meeting is the first LMS meeting on inverse problems (in a series of four in 2014) that brings together UK researchers who work on advancing the field of inverse problems, both from a theoretical and from an applied point of view.
The meeting will concentrate on sparse regularisation of inverse problems. Regularisation is one major technique for the solution of ill-posed inverse problems. It imposes sufficient constraints on the solution to allow for a stable inversion. In recent years ideas from compressed sensing and sparse reconstruction have entered inverse problems research with the development of inversion models that feature a regularisation which imposes certain sparsity constraints on the solution. In particular, this meeting will concentrate around the major themes:
- Modelling of sparsity
- Non-smooth regularisation and geometric priors
- Sparse sampling
- Sparse regularisation in practice
Student Poster Prize
A prize of £100 will be awarded to the best student poster to support travel and accommodation costs (sponsored by Cambridge's Department of Applied Mathematics and Theoretical Physics).