Wavelet image denoising practice has shown that the performance of
simple estimators may be substantially improved by averaging these
estimators over a collection of transformations such as translations
or rotations. In this paper, we explain and quantify these empirical
findings using estimation theory. We consider a general nonlinear observation model, analyze the estimation risk of transformation-averaged estimators, and derive an upper bound on the risk reduction due to transformation averaging. The bound is evaluated for several estimators, using different averaging strategies (including a randomized strategy) and different wavelet bases. The practical usefulness of the bound is established for standard image denoising examples.