This paper examines the estimation of an indirect signal embedded in white noise
on vector bundles. It is found that the sharp minimax bound is determined by the
degree to which the indirect signal is embedded in the linear operator. Thus when
the linear operator has polynomial decay, recovery of the signal is polynomial where the exact minimax constant and rate are determined. Adaptive sharp estimation is carried out using a blockwise shrinkage estimator. Application to the spherical deconvolution problem for the ordinary smooth case is made.