
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 Xray 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:
 Mathematical tools
(Radon transforms, Fourier transforms etc.)
 Reconstruction
algorithms.
 Resolution, accuracy,
illposed problems, incomplete data and other practical matters.
 3D imaging.
 Scattering and inverse
scattering for the wave equation.
 Physical background and
the formulation of the problem.
 Theories of
GelfandLevitan and Marchenko.
Starting date:
Tuesday, October 29, 2002
Time: 17:00, every Tuesday
Place: School of Mathematics, IPM,
Nivaran Sqr.,
Tehran, Iran.
 