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

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.