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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENTAL SEMINAR}
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\centerline{4:15 p.m., Tuesday, July 25, 2000}
\centerline{Sequoia Hall Rm. 200}
\centerline{(Cookies at 3:45 p.m. in 1st Floor Lounge)}

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\centerline{\sl Larry Shepp}
\centerline{\sl Rutgers University}
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\centerline{\bf From emission tomography to fMRI}
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In emission tomography a radiopharmaceutical moves under metabolic action
to lodge in tissues active during a task; the emitted radioactivity then
can be traced and the metabolism studied for clinical use. 

In principle we could use this technique to learn which parts of the brain
are active during a higher cognition task such as image recognition. One
problem with emission CT is that it has inherently poor temporal
resolution. Since image recognition involves several subtasks which should
be separated, emission CT is not adequate to this higher cognition study.

Functional magnetic resonance imaging is a more recent technique which can
also be used to study the same problem. In fMRI oxy-hemoglobin and
deoxy-hemoglobin have a slightly different magnetic resonance signature.
Mathematically a measurement is made of the Fourier transform at various
points k of the difference f between pre and post task level of
oxy-hemoglobin. Each measurement of the Fourier transform of f at a point takes
about 1 ms. If we use a dense grid of points k we can reconstruct the
difference via Fourier inversion but it takes too long to measure the
transform at a dense grid. Instead we propose to measure the transform only
at a relatively few points and then to use these measurements to compute
only a low spatial resolution image of f. That is we are trading off
spatial for temporal resolution. We use wavelets or more precisely prolate
spheroidal wave functions to realize the trade-off. This is joint work with
CH Zhang of Rutgers and Qing Yang at Hershey Medical Center.

Martin Lindquist may present part of his thesis at Rutgers which is based
on his new L1 formulation of the problem at the end of my talk and may
describe his on-going work at Stanford and Hershey Medical Centers. 

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