Unsupervised Regression for Image Denoising
Speaker: Martin Raphan , New York University (NYU)Contact:
Date: February 14 2008
Time: 1:00PM to 2:00PM
Host: C. Mario Christoudias, Gerald Dalley, MIT CSAIL
C. Mario Christoudias, Gerald Dalley, 3-4278, 3-6095, firstname.lastname@example.org, email@example.comRelevant URL:
NOTE THE (FINAL) TIME CHANGE
Title: Unsupervised Regression for Image Denoising
There are two standard frameworks for describing optimal least squares
estimation of a random quantity from corrupted measurements. The first
technique, Bayesian Least Squares (BLS) estimation, uses explicit models
of both the corruption process and the prior distribution of the quantity
to be estimated in order to formulate an optimal estimator via Bayes'
rule. The second technique, Least Squares regression, uses supervised
training on a data set, which has clean samples paired with corrupted
versions of those samples, to choose an optimal estimator from some
family. In many applications, however, one has available neither a model
of the prior distribution, nor uncorrupted measurements of the variable
being estimated. We will describe a framework for expressing the BLS
estimator (regression function) entirely in terms of a model of the
corruption process and the density of the *corrupted* measurements.
We show a practical implementation of this nonparametric estimator for
additive white gaussian noise (AWGN), and demonstrate the use of this
procedure for denoising photographic images, showing that it compares
favorably with previously published methods which use explicit prior
models. We also describe a dual, prior-free formulation of the Mean
Square Error (MSE) which generalizes Stein's Unbiased Risk estimator
(SURE), and show how this may be used to perform *unsupervised*
regression, based only on samples of the corrupted signal. We then
demonstrate the use of this dual formulation in image denoising.
Finally, we use the dual formulation to prove the empirically observed
fact that, despite their suboptimality, marginal image denoisers chosen
to minimize MSE within the subbands of a redundant multi-scale
decomposition will always perform better than on the orthonormal versions
of those bases. We also develop an extension of SURE that allows
minimization of the image-domain MSE for estimators that operate on
subbands of a redundant decomposition, and show that this gives
improvement over methods which optimize MSE within subbands.
This talk is being held in a non-standard location (32-D507) and at a non-standard time (11am).
If you would like to meet with Martin on 14 Feb, please email Maysoon (firstname.lastname@example.org). She will be coordinating the visit.
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