A Course/Seminar:

INVERSE PROBLEMS

Mehrdad Shahshahani

Professor of IPM

Broadly speaking, Inverse Problems are about obtaining information regarding an object or phenomenon that is not directly accessible or observable.  Perhaps the most publicized inverse problem in mathematics is, Can one hear the shape of a drum?  Inverse problems have a wide range of applications in sciences.  In medical sciences, there is the problem of interpreting CAT scan, PET, fMRI or other medical imaging data.  An essential feature of these problems is the inversion of the Radon Transform.  Understanding the structure of DNA or other molecules from the X-ray diffraction data are examples of inverse problems.  In geophysics, the shock waves of an earthquake provide information about the structure the earth.  In physics there is the problem of the determination of a potential from the scattering data.

The purpose of the course/seminar is to provide the background material for the IPM workshop on Inverse Problems scheduled for February 2003.  Several distinguished experts are expected to attend the meeting.  To benefit from the meeting, students are encouraged to familiarize themselves with the background material so that they can interact scientifically with the experts at the meeting.

The course meets once a week for two hours (tentatively scheduled for Tuesdays at 5 pm, at IPM, Niavaran).  The syllabus for the course is as follows:

1. Mathematical tools (Radon transforms, Fourier transforms etc.)
2. Reconstruction algorithms.
3. Resolution, accuracy, ill-posed problems, incomplete data and other practical matters.
4. 3-D imaging.
5. Scattering and inverse scattering for the wave equation.
6. Physical background and the formulation of the problem.
7. Theories of Gelfand-Levitan and Marchenko.

Starting date:

Tuesday, October 29,  2002

Time: 17:00, every Tuesday

Place:  School of Mathematics, IPM,

            Nivaran Sqr.,

            Tehran, Iran.