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%T Limited data problems for the generalized Radon transform in R^n.
%A Quinto, Eric Todd.; Frikel, Jürgen.
%8 2016-08-30
%I Tufts University. Tisch Library.
%R http://localhost/files/n8710301z
%X We consider the generalized Radon transform (defined in terms of smooth weightfunctions) on hyperplanes in Rn. We analyze general filtered backprojection type reconstructionmethods for limited data with filters given by general pseudodifferential operators. We providemicrolocal characterizations of visible and added singularities in Rn and define modified versionsof reconstruction operators that do not generate added artifacts. We calculate the symbol of ourgeneral reconstruction operators as pseudodifferential operators and provide conditions for the filtersunder which the reconstruction operators are elliptic for the visible singularities. If the filters arechosen according to those conditions, we show that almost all visible singularities can be recoveredreliably. Our work generalizes the results for the classical line transforms in R2 and the classicalreconstruction operators (that use specific filters). In our proofs, we employ a general paradigm thatis based on the calculus of Fourier integral operators. Since this technique does not rely on explicitexpressions of the reconstruction operators, it enables us to analyze more general imaging situations.
%[ 2018-10-08
%9 Text
%~ Tufts Digital Library
%W Institution