Bayesian multiresolution filter design

This paper discusses a multiresolution approach to Bayesian design of binary filters. The key problem with Bayesian design is that for any window one needs enough observations of a template across the states of nature to estimate its prior distribution, thus introducing severe constraints on single window Bayesian filter designs. By using a multiresolution approach and optimized training methods, we take advantage of prior probability information in designing large-window multiresolution filters. The key point is that we define each filter value at the largest resolution for which we have sufficient prior knowledge to form a prior distribution for the relevant conditional probability, and move to a sub-window when a non-uniform prior is not available. This is repeated until we are able to make a filtering decision at some window size with a known prior for the probability P(Y equals 1x), which is guaranteed for smaller windows. We consider edge noise for our experiments with emphasis on realistically degraded document images.