## Abstract for May 2, 2006

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Tatiana Soleski (IMA, University of Minnesota)

In Computerized Tomography (CT), an image must be reconstructed
from data given by the Radon transform of the image. In this talk we
introduce a method of recovering the image based on the sampling
properties of the Prolate Spheroidal wavelets (PS-wavelets) which are
superior to other wavelet systems. It avoids integration and allows the
precomputation of certain coefficients. The approximation based on this
method is shown to converge to the true image under mild hypotheses. The
algorithm is then tested on the standard Shepp-Logan image and is shown to
be surprisingly good.
Another interesting issue is related to the construction of the above
mentioned wavelets. The standard way of calculating their values uses an
approximation based on Legendre polynomials and Bessel functions. We
present a new method based on an eigenvalue problem for a matrix operator
equivalent to that of the integral operator associated with the
PS-wavelets. Its solution gives the values of these functions on the
entire real line and is computationally more efficient.

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