Empirical Bayes Least Squares Estimation without an Explicit Prior
Martin Raphan, Eero P. Simoncelli, Courant Inst · 2007
Bayesian estimators are commonly constructed using an explicit priormodel. In many applications, one does not have such a model, and it isdifficult to learn since one does not have access to uncorrupt ed measure-ments of the variable being estimated. In many cases however, includingthe case of contamination with additive Gaussian noise, the Bayesianleast squares estimator can be formulated directly in terms of the distri-bution of noisy measurements. We demonstrate the use of this formu-lation in removing noise from photographic images. We use a local ap-proximation of the noisy measurement distribution by exponentials overadaptively chosen intervals, and derive an estimator from this approxi-mate distribution. We demonstrate through simulations that this adaptiveBayesian estimator performs as well or better than previously publishedestimators based on simple prior models.