  Attenuated Radon projections with respect to the weight function $W_\mu(x,y)
= (1-x^2-y^2)^{\mu-1/2}$ are shown to be closely related to the orthogonal
expansion in two variables with respect to $W_\mu$. This leads to an algorithm
for reconstructing two dimensional functions (images) from attenuated Radon
projections. Similar results are established for reconstructing functions on
the sphere from projections described by integrals over circles on the sphere,
and for reconstructing functions on the three-dimensional ball and cylinder
domains.
