The stability estimates of the inverse problem for the weighted Radon transform

ABSTRACT

In this paper, we get some new properties of the weighted Radon transform by Fourier transform, convolution, Riesz potential, and so on. Meanwhile, the results of Natterer are generalized to non-uniform attenuation. Furthermore we study the Sobolev estimation of the n-dimensional non-uniform attenuation Radon transform and its dual operator by the Young's inequality. Then, we extend conclusions of Rigaud and Lakhal to the n-dimensional space. Finally, the results of Sharafutdinov are generalized to non-uniform attenuation.

KEYWORDS:

• Hilbert space
• Sobolev estimation
• convolution
• Riesz potential
• weighted radon transform

2010 MR SUBJECT CLASSIFICATIONS:

• 65R32
• 68W25
• 65F22

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This project is supported by the National Natural Science Foundation of China (Nos. 11871481, 62071262), China Scholarship Council (No. 201906380034) and K. C. Wong Magna Fund in Ningbo University.