Bayes Risk Reduction of Estimators Using Artificial Observation Noise

This paper studies noise enhanced (NE) estimators, which are constructed from an original estimator by artificially adding noise to the observation and computing the expected estimator output. By this expectation operation, we take into account the neighbourhood of an observation and the resulting NE estimator often has a smaller Bayes risk than the original one. We derive some general properties of this estimator and also present a method to obtain a suitable approximation of the optimal NE estimator which can be computed numerically by solving a constrained optimization problem. Finally, we study two examples to show the Bayes risk improvement that we can obtain from the NE estimator and we compare it to the stochastic resonance estimator.