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2000-2001
MATHEMATICS COLLOQUIUM SERIES
9/19/00 Colloquium
Mathematical analysis of an efficient algorithm for spiral tomography
Abstract: In this talk I will describe an efficient filtered back projection (FBP) algorithm for inversion of spiral cone beam data, discuss its theoretical properties, and illustrate performance of the algorithm by numerical examples. In particular, it is shown that the algorithm does not reconstruct f exactly, but computes the result of applying a pseudo-differential operator (PDO) with singular symbol to f. Away from critical directions the amplitude of this PDO is homogeneous of order zero in the dual variable, bounded, and approaches one as the pitch of the spiral goes to zero. Numerical experiments show that even when the pitch is relatively large, the accuracy of reconstruction is quite high. On the other hand, under certain circumstances, the algorithm produces artifacts typical of all FBP-type algorithms.