Local algorithms in exterior tomography

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 phe...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2007-02, Vol.199 (1), p.141-148
Main Author: Quinto, Eric Todd
Format: Article
Language:English
Subjects:
Exact sciences and technology
Exterior Radon transform
Integral transforms, operational calculus
Lambda Tomography
Limited data tomography
Mathematical analysis
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Microlocal analysis
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Sciences and techniques of general use
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Summary: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.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2004.11.055