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 subwindow when a nonuniform 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=1|x), which is guaranteed for smaller windows. The optimized training algorithm overcomes computational issues that are associated with larger window filter designs. Further the Bayesian multiresolution filter is compared with the differencing multiresolution filter. The robustness of the Bayesian design is demonstrated over variation of the distributions of the states of nature. We consider edge noise for our experiments with emphasis on realistically degraded document images.