Applications of inverse problems are already well-developed in several domains of physical sciences since they date back to the beginning of the research in this area of applied mathematics. In most physical experiments the data are given by the convolution of the impulse response of the instrument with the physical quantity under investigation; the latter can be obtained by solving the ill-posed problem of data deconvolution. Another frequently used technique consists in illuminating a physical system by means of some kind of radiation and detecting the scattered waves. The constitution of the object can be obtained by solving the so-called inverse scattering problems, also ill-posed. The first example of these problems dates back to the beginning of nuclear physics, namely the attempt of determining the nucleon-nucleon potential from scattering data.
The aim of the workshop is to provide exhaustive surveys of some of the most important applications. Therefore the workshop consists of general-type talks, presenting the state of the art, the perspectives and the open problems of specific physical applications of inverse problems methods. These can range from microscopy and astronomy to atmosphere and Earth sciences, to rheology, medical imaging etc. It is obvious that there is an important intersection between the topics of this workshop and those of the following ones on imaging and life sciences. The talks on image deconvolution and brain imaging emphasize these links.
(University of Illinois at Urbana-Champaign, Electrical and Computer Engineering)
Tony Chan (UCLA, Mathematics)
Frank Natterer (University of Muenster, Germany, Mathematics)
Robert Plemmons (Wake Forest University, Math and Computer Science)
Stefano Soatto (UCLA, Computer Science)