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Shen, Zhengjie; Wang, Jinping

The research of complex analytic method in spect image reconstruction. (English) Zbl 1310.44006

Appl. Anal. 93, No. 11, 2451-2461 (2014).
Summary: We successfully extend Natterer’s results to the attenuated Radon transform with imaginary coefficients. And by means of the theory of complex analysis and integral transform, we study the inversion of two-dimensional weighted Radon transform and derive similar explicit inversion formulas with two different methods, which are closely related to Novikov’s inversion formula.

Cited in 7 Documents

MSC:

44A12 Radon transform
44A15 Special integral transforms (Legendre, Hilbert, etc.)
65R32 Numerical methods for inverse problems for integral equations
30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane

Keywords:

the attenuated Radon transform; weighted Radon transform; Novikov’s inversion formula; complex analysis; integral transform
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References:

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