  We consider the problem of recovering a signal observed in Gaussian noise. If
the set of signals is convex and compact, and can be specified beforehand, one
can use classical linear estimators that achieve a risk within a constant
factor of the minimax risk. However, when the set is unspecified, designing an
estimator that is blind to the hidden structure of the signal remains a
challenging problem. We propose a new family of estimators to recover signals
observed in Gaussian noise. Instead of specifying the set where the signal
lives, we assume the existence of a well-performing linear estimator. Proposed
estimators enjoy exact oracle inequalities and can be efficiently computed
through convex optimization. We present several numerical illustrations that
show the potential of the approach.
