  We review and extend a technique for recovering a smooth function from its
averages over a wide class of curves in a general region of Euclidean space.
The method is based on complexification of the underlying vector fields
defining the transport and recasting the problem in terms of complex-analytic
function theory. Conditions on the validity of prior formulae appearing in a
previous paper as well as stability estimates are then discussed first for the
case of vector fields with polynomial coefficients and later for more general
cases.
