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Phone: (407) 823-6284;   Fax: (407) 823-6253;   MAP  207 2006-2007 MATHEMATICS COLLOQUIUM SERIES 11/28/06 Colloquium Mikhail Kapralov University of Central Florida Efficient inversion of the cone beam transform for a general class of curves Abstract:  We extend an efficient cone beam transform inversion formula, proposed earlier for helices, to a general class of curves. The conditions that describe the class are very natural. Curves C are smooth, without self-intersections, have positive curvature and torsion, do not bend too much in a certain sense, and do not admit lines which are tangent to C at one point and intersect C at another point. A domain U is found where reconstruction is possible with a filtered backprojection type algorithm. Results of numerical experiments demonstrate very good image quality. The algorithm developed is useful for image reconstruction in computerized tomography.