In the last twenty years the field of inverse problems has undergone rapid development. These are problems where the solutions are nearly always indirectly related to the available data, where causes are determined for desired or observed effects. The problems are often ill-posed in that small changes in the data can produce large effects in the solution. Furthermore, even questions of whether a solution that corresponds to likely noisy data can exist and how many and how different solutions there may be that correspond to partial data sets need to be considered.
The enormous increase in computing power and the development of powerful algorithms has made it possible to consider real-world problems of growing complexity and has led to a growing appetite to apply the techniques of inverse problems to ever more complicated physical and biological problems. Applications include several medical as well as other imaging techniques, location of oil and mineral deposits in the earth’s substructure, creating astrophysical images from telescope data, finding cracks and interfaces within materials, shape optimization, and model identification in growth processes and more recently in the life sciences. Historically the model of the physical phenomena was frequently linear with the inverse problem being nonlinear; recent work also includes nonlinear physical phenomena models.
The goal in this workshop is to include a broad spectrum of advancing new problems with presentations on both computational and theoretical issues and for a wide range of applications. The conference also serves as a lead-in to the IPAM long program on Inverse Problems.
This conference is the second in a series of conferences on this subject, following the first one held in Montecatini in 2001.
(Case Western Reserve University)
Heinz Engl (Johannes Kepler University, Austria)
Joyce McLaughlin, Chair (Rensselaer Polytechnic Institute)