Empirical Bayes least squares estimation without an explicit prior
Published in:
Technical Report TR2007-900, May 2007
Computer Science Department,
Courant Institute of Mathematical Sciences
New York University
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.
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