A new complex approach towards approximate inverse and generalized Radon transform

Abstract

In this paper, we first consider the framework of Sobolev spaces and derive analytically a reconstruction algorithm by means of the residue theorem of complex analysis, the approximate inverse, Gaussian mollifier and integral equations. And we successfully extend Natterer’s results to the generalized Radon transform with non-uniform attenuation. Finally, we investigate the smoothing properties of the generalized Radon transform.

Keywords:

• Residue theorem
• Sobolev spaces
• generalized Radon transform
• integral equation

AMS Subject Classifications:

• 30E25
• 65R32
• 65F22

Acknowledgements

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

Notes

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 [grant number 61271398], K. C. Wong Magna Fund in Ningbo University and and the Scientific Research Foundation of Graduate School of Ningbo University [grant number G17068].