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Inversion of the exponential X‐ray transform. I: Analysis
Author(s) -
Hazou Irene A.,
Solmon Donald C.
Publication year - 1988
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670100506
Subject(s) - mathematics , radon transform , exponential function , inversion (geology) , exponential decay , convolution (computer science) , projection (relational algebra) , mathematical analysis , exponential type , algorithm , physics , artificial intelligence , paleontology , structural basin , artificial neural network , nuclear physics , computer science , biology
The exponential X‐ray transform arises in single photon emission computed tomography and is defined on functions on ℝ n by, where μ is a constant. Approximate inversion, and inversion formulae of filtered back‐projection type are derived for this operator in all dimensions. In particular, explicit formulae are given for convolution kernels (filters) K corresponding to a general point spread function E that can be used to invert the exponential X‐ray transform via a filtered back‐projection algorithm. The results extend and refine work of Tretiak and Metz 17 .