Stability estimates with a priori bound for the inverse local Radon transform

2014/05/15 by Joel Andersson, Andersson, Joel, Jan Boman +1
Computer Science · Mathematics · Medicine · #44A12 #92C55 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Medical Imaging Techniques and Applications #Numerical methods in inverse problems #math.AP #msc:44A12 #msc:92C55

paper · pdf · doi:10.48550/arxiv.1405.3922

34 pages

arxiv created 2014/05/15 · openalex publication_date 2014/05/15 · arxiv updated 2014/05/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We consider the inverse problem for the 2-dimensional weighted local Radon transform R_m[f], where f is supported in y≥ x² and R_m[f](ξ,η)=∫ f(x, ξx + η) m(ξ, η, x) d x is defined near (ξ,η)=(0,0). For weight functions satisfying a certain differential equation we give weak estimates of f in terms of R_m[f] for functions f that satisfies an a priori bound.

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