8 May 2001 Bayesian iterative binary filter design
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Abstract
Optimal translation-invariant binary windowed filters are determined by probabilities of the form P(Y equals 1|x), where x is a vector (template) of observed values in the observation window and Y is the value in the image to be estimated by the filter. The optimal window filter is defined by y(x) equals 1 if P(Y equals 1|x) (greater than) 0.5 and y(x) equals 0 if P(Y equals 1|x) (less than or equal to) 0.5, which is the binary conditional expectation. The fundamental problem of filter design is to estimate P(Y equals 1|x) from data (image realizations), where x ranges over all possible observation vectors in the window. A Bayesian approach to the problem can be employed by assuming, for each x, a prior distribution for P(Y equals 1|x). These prior distributions result from considering a range of model states by which the observed images are obtained from the ideal. Instead of estimating P(Y equals 1|x) directly from observations by its sample mean relative to an image sample, P(Y equals 1|x) is estimated in the Bayesian fashion, its Bayes estimator being the conditional expectation of P(Y equals 1|x) given the data. Recently the authors have shown that, with accurate prior information, the Bayesian multiresolution filter has significant benefits from multiresolution filter design. Further, since the Bayesian filter is trained over a wider range of degradation levels, it inherits the added benefit of filtering a degraded image at different degradation levels in addition permitting iterative filtering. We discuss the necessary conditions that make a binary filter a good iterative filter and show that the Bayesian multiresolution filter is a natural candidate.
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Vishnu G. Kamat, Vishnu G. Kamat, Edward R. Dougherty, Edward R. Dougherty, } "Bayesian iterative binary filter design", Proc. SPIE 4304, Nonlinear Image Processing and Pattern Analysis XII, (8 May 2001); doi: 10.1117/12.424975; https://doi.org/10.1117/12.424975
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