Local algorithms in exterior tomography

Authors:
Eric Todd Quinto
Affiliations:
Department of Mathematics, Tufts University, Medford, MA
Venue:
Journal of Computational and Applied Mathematics - Special issue: Special functions in harmonic analysis and applications
Year:
2007

Citing 9
Cited 0

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Abstract

Exterior tomographic data are taken over lines outside a central region, and such data occur in the industrial nondestructive evaluation of large objects such as rockets. We explain, using microlocal analysis, which singularities are well reconstructed from exterior data, and we explain how this phenomenon is reflected in the singular value decomposition for the exterior transform [E.T. Quinto, Singular value decompositions and inversion methods for the exterior Radon transform and a spherical transform, J. Math. Anal. Appl. 95 (1983) 437-448]. We extend Lambda Tomography to exterior data and to limited angle exterior data. The algorithm is tested on industrial data from Perceptics, Inc.