Limited data problems for the generalized Radon transform in $mathbb{R}^n$

We consider the generalized Radon transform (defined in terms of smooth weight functions) on hyperplanes in $mathbb{R}^n$. We analyze general filtered backprojection type reconstruction methods for limited data with filters given by general pseudodifferential operators. We provide microlocal characterizations of visible and added singularities in $mathbb{R}^n$ and define modifi