  Our focus is on robust recovery algorithms in statistical linear inverse
problem. We consider two recovery routines - the much studied linear estimate
originating from Kuks and Olman [42] and polyhedral estimate introduced in
[37]. It was shown in [38] that risk of these estimates can be tightly
upper-bounded for a wide range of a priori information about the model through
solving a convex optimization problem, leading to a computationally efficient
implementation of nearly optimal estimates of these types. The subject of the
present paper is design and analysis of linear and polyhedral estimates which
are robust with respect to the uncertainty in the observation matrix. We
evaluate performance of robust estimates under stochastic and deterministic
matrix uncertainty and show how the estimation risk can be bounded by the
optimal value of efficiently solvable convex optimization problem; "presumably
good" estimates of both types are then obtained through optimization of the
risk bounds with respect to estimate parameters.
