Stability estimates for the local Radon transform. (12th February 2018)

• Record Type: Journal Article
• Authors: Andersson, Joel; Boman, Jan
• Is Part Of: Inverse problems. Volume 34:Number 3(2018:Mar.)
• Publication Date: 2018-02-12
• Subjects: radon transform -- local injectivity -- stability estimates; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aaa99c
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: 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 ] ( ξ, η ) = ∫ f ( x, ξ x + η ) d x is defined near ( ξ, η ) = ( 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 | f ] ( ξ, η ) = ∫ f ( x, ξ x + η ) m ( ξ, η, x ) d x .