[BIC-announce] Talk to be given by Dr. Rolf Clackdoyle - Classical tomography is (sort of) Local after all!

[Jennifer Chew, Ms.]

SPEAKER:  Dr. Rolf Clackdoyle (Directeur de Recherche, Centre National de la Recherche Scientifique)
(member of the CNRS-Saint Etienne University mixed research unit, the Laboratoire Hubert Curien)

DATE:  Thursday, September 2, 2010
TIME;  2:30 P.M.
PLACE:  de Grandpre Communications Centre

Abstract of talk given below this message.

Jennifer Chew
McConnell Brain Imaging Centre
MNI - WB317
3801 University Street
Montreal, Qc  H3A 2B4
Telephone:  514-398-8554
Fax:  514-398-2975



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Title:   Classical Tomography is (sort of) Local after all!
Abstract:
Many medical scanners present (at least to first order) the same
mathematical problem: how can the density function of the scanned object
be recovered from the measurements, which are essentially summed densities
taken over various straight lines? This problem arises in tomographic
nuclear medicine imaging (PET and SPECT) and in x-ray imaging (CT).

In the classical situation, a single slice is to be reconstructed from
line-integrals constrained to the slice of interest. The solution to this
mathematical problem was re-established in the 1970's by researchers
unaware that it was just the 2D version of a solution given by J. Radon
in 1917.

In the general version, Radon's formulas showed that in odd dimensions
(in 3D, 5D, 7D, ...) the problem is "local" in the sense that measurements
only need to be taken 'near' the region of interest; whereas in even
dimensions all measurements are required, including measurement lines far
from the region of interest.

As an example: if classical (2D) tomography were somehow "local" then a
CT of the heart would only need x-ray passing through the heart. However,
Radon's formula indicates that all x-rays in the tomographic slice must
be measured including, for example, rays that pass through the liver
but miss the heart.

In a surprising mathematical development in 2002, it has been established
that, even though classical tomographic is two dimensional, some degree
of local behavior can occur. In some cases, accurate reconstruction
can be obtained from local information. This talk will describe current
findings, and indicate consequences for reduced dose and/or improved
handling of noisy measurements in region-of-interest tomography.
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