Abstract for May 2, 2006

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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