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ABSTRACT
In this paper, we first study the smoothing properties of the attenuated Radon transform with complex-valued coefficients. Then on the basis of the framework of Sobolev spaces and the method of the approximate inverse, we derive a reconstruction algorithm. Finally, we extend the results of Rigaud and Lakhal to the attenuated Radon transform with complex-valued coefficients.
Acknowledgements
The authors gratefully acknowledge Prof. Du Jinyuan for his assistance and extremely instructive suggestion in this research.
Disclosure statement
No potential conflict of interest was reported by the authors.
Additional information
Funding
This project is supported by the National Natural Science Foundation of China [number 61271398], K. C. Wong Magna Fund in Ningbo University and the Scientific Research Foundation of Graduate School of Ningbo University [grant number G17068].