Applied Math Seminar
Spring Quarter 2001
3:15 - 4:15 p.m.
Sloan Mathematics Corner
Building 380, Room 380-C

June 8, 2001


F. Alberto Grunbaum
University of California, Berkeley

Diffuse tomography : an nonlinear inverse
problem in medical imaging

Abstract:

The usual problem in X-ray tomography consists of recovering a function (the attenuation coefficient as a function of the spatial variables) from its line integrals. This gives a linear inverse problem whose solution has revolutionized diagnostic medicine in the last 30 years.

For certain problems it is convenient to use a very low energy source, like an infrared laser. In this situation one can no longer ignore the scattering of the probing radiation by the medium and one needs to solve simultaneously for the absorption and scattering characteristics of the tissue. This results in a formidable nonlinear inversion problem which is orders of magnitude harder than its linear version.

Early work in this field is already being used in a hospital enviroment both for mammographies as well as in a neonatal clinic.

I will discuss some highly simplified models of the actual situation and present some results that indicate both the complexity of the problem as well as the fact that mathematics can play a useful role in this emerging field.

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