%0 Journal Article
%T Partial Radon Transform and Hamburger moment completion in $\mathbb{R}^2$
%A Hayoung Choi
%A Farhad Jafari
%J Mathematics
%D 2015
%I arXiv
%X The Radon transform is one of the most powerful tools for reconstructing data from a series of projections. Reconstruction of Radon transform with missing data can be closely related to reconstruction of a function from moment sequences with missing terms. A new range theorem is established for the Radon transform $Rf$ on $L^1$ based on the Hamburger moment problem in two variables, and the sparse moment problem is converted into the Radon transform with missing data and vice versa. A modified Radon transform for missing data is constructed and an inversion formula is established.
%U http://arxiv.org/abs/1511.02523v1