The research of complex analytic method in spect image reconstruction

Abstract

In this paper, 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.

Keywords:

• the attenuated Radon transform
• weighted Radon transform
• Novikov’s inversion formula
• complex analysis
• integral transform

AMS Subject Classifications:

• 44A15
• 65R32
• 30E20

Acknowledgements

The authors gratefully acknowledge Prof. Du Jinyuan for his assistance and extremely instructive suggestion in this research.

Notes

This article is dedicated to Professor Wei Lin on the occasion his 80th birthday.

This project is supported by the National Natural Science Foundation of China [grant number 61271398] and K. C. Wong Magna Fund in Ningbo University.