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

被引：2
|
作者：
Li, Wei [1 ]
Xian, Jun [1 ]
Wang, Jinping [2 ]
机构：
[1] Sun Yat Sen Univ, Sch Math, Guangzhou, Peoples R China
[2] Ningbo Univ, Sch Math & Stat, Ningbo, Peoples R China
来源：
APPLICABLE ANALYSIS | 2023年 / 102卷 / 06期
基金：
中国国家自然科学基金;
关键词：
Hilbert space; Sobolev estimation; convolution; Riesz potential; weighted radon transform; RECONSTRUCTION; ALGORITHM; CONVERGENCE;
D O I：
10.1080/00036811.2021.1994957
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：1673 / 1686
页数：14
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