Stability estimates for the local Radon transform

被引：1

作者：

Andersson, Joel ^{[1
]}

Boman, Jan ^{[1
]}

机构：

[1] Stockholm Univ, Dept Math, SE-10691 Stockholm, Sweden

来源：

INVERSE PROBLEMS | 2018年 / 34卷 / 03期

关键词：

radon transform; local injectivity; stability estimates; INVERSION-FORMULA;

D O I：

10.1088/1361-6420/aaa99c

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the inverse problem for the 2-dimensional local Radon transform R[f], where f is supported in y >= x(2) and R[f](xi, eta) = integral f (x, xi x + eta) dx is defined near (xi, eta) = (0, 0). We give logarithmic estimates of f in terms of R[f] for functions f that satisfy an a priori bound. For a certain class of smooth, positive weight functions m we give similar estimates for the weighted Radon transform R-m vertical bar f](xi, eta) = integral f (x, xi x + eta) m(xi, eta, x) dx.

引用

页数：23

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