Title: Empirical Bayes least squares estimation without an explicit prior


Authors: Martin Raphan and Eero P. Simoncelli 

Bayesian estimators are commonly constructed using an explicit prior
model.  In many applications, one does not have such a model, and it is
difficult to learn since one does not have access to uncorrupted
measurements of the variable being estimated.  In many cases however,
including the case of contamination with additive Gaussian noise, the
Bayesian least squares estimator can be formulated directly in terms of
the distribution of noisy measurements.  We demonstrate the use of
this formulation in removing noise from photographic images.  We
use a local approximation of the noisy measurement distribution by
exponentials over adaptively chosen intervals, and derive an estimator
from this approximate distribution.  We demonstrate through simulations
that this adaptive Bayesian estimator performs as well or better than
previously published estimators based on simple prior models.