Theoretical and Computational Approaches to Large Scale Inverse Problems

Edinburgh, 2nd-4th December 2015

Main organisers: Simon Arridge, John Aston, Peter Richtarik, Carola-Bibiane Schönlieb, Andrew Stuart, Jared Tanner

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Inverse Problems (IP) is at the heart of data science. It is cross-disciplinary both within mathematics, encompassing aspects of pure, applied and statistics, and across subjects, including physical sciences, engineering, medicine and biology to name only a few. Inverse problems arise in almost all fields of science when details of a postulated model have to be determined from a set of observed data. With inverse problems, scientists observe an effect and work to determine the cause; the ultimate goal is to find essential information (an object or material properties) that are hidden within a possible wealth of measurements.  Biomedical imaging, for instance, gives rise to a variety of inverse problems in which the common goal is to compute an image that visualises the interior of a living organism.
Some inversion approaches are based on effective use of a mathematical model in order to make optimal use of the data; other approaches involve model-blind data mining methods. Since inverse problems are concerned with the processing of data and extraction of relevant information, the field is considered part of Information Technology. Inverse problems are mathematically hard, since they are highly nonlinear, ill-posed and present important challenges of deep mathematical interest which are key to the development of reliable and accurate practical solution methods. Often the observed data is noisy, of large scale and high dimensional, and there is a significant challenge in determining the statistical properties of any proposed inversion.