Inversion of the exponential X‐ray transform. I: Analysis | Zendy

Hazou Irene A. | Zendy; Solmon Donald C. | Zendy

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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 .

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