Mathematical Methods in Emerging Modalities of Medical Imaging (09w5017)

Objectives

The workshop will assemble leading researchers from mathematics, physics, engineering and medicine interested in developing and implementing mathematical methods of novel medical diagnostic imaging, as well as junior scientists entering this exciting field. Among the techniques to be discussed, one can mention, for instance, optical tomography, electron tomography, phase contrast CT, thermo/photoacoustic tomography, elastography, ultrasound modulated optical tomography, and electrical impedance tomography. These new modalities of imaging involve combinations of different challenging problems on crossroads of mathematics, physics, and engineering. Several of them have already lead to new developments in mathematics, and most introduce mathematical
problems which have not yet been resolved, or often even considered. For instance, despite recent progress, many mathematical issues of photoacoustic imaging (a modality that combines electromagnetic and ultrasound waves), have not been resolved. One can name in particular reconstructions in presence of a background that is inhomogeneous with respect to ultrasound waves. Another token example is ultrasound modulated optical tomography, which lacks developed reconstruction methods.

The goal is to formulate the mathematical problems that must be resolved to meet outstanding challenges of this young and fast developing area and to assess and facilitate the current progress in these directions. It is expected that topics to be discussed would include, in particular, formulation of appropriate mathematical models, problems of uniqueness and stability of reconstruction, reconstruction formulas and numerical algorithms, incomplete data problems, etc.

In spite of quite a few tomography and inverse problem conferences, no meeting of this kind seems to have taken place, while the need for it is, and benefits of having it will be significant.

It is expected that meeting of such a group and the resulting creative discussions will lead to faster advances in this area that is crucial for medicine, as well for industrial non-destructive evaluation and geological prospecting. New collaborations will be created across the fields that will facilitate further successes. Thus, it is believed that the proposed meeting is timely and important.