  We consider the problem of recovering linear image of unknown signal
belonging to a given convex compact signal set from noisy observation of
another linear image of the signal. We develop a simple generic efficiently
computable nonlinear in observations "polyhedral" estimate along with
computation-friendly techniques for its design and risk analysis. We
demonstrate that under favorable circumstances the resulting estimate is
provably near-optimal in the minimax sense, the "favorable circumstances" being
less restrictive than the weakest known so far assumptions ensuring
near-optimality of estimates which are linear in observations.
