Design and analysis of robust binary filters in the context of a prior distribution for the states of nature

An optimal binary-image filter estimates an ideal random set by means of an observed random set. A fundamental and practically important question regards the robustness of a designed filter: to what extent does performance degrade when the filter is applied to a different model than the one for which it has been designed? By parameterizing the ideal and observation random sets, one can analyze the robustness of filter design relative to parameter states. Based on a prior distribution for the states, a robustness mesure is defined for each state in terms of how well its optimal filter performs on models for different states. Not only is filter performance on other states taken into account, but so too is the contribution of other states in terms of their mass relative to the prior state distribution. This paper characterizes maximally robust states, derives performance bounds, treats mean robustness (as opposed to robustness by state), introduces a global filter that is applied across all states, particularizes the entire analysis to a sparse noise model for which there are analytic robustness expressions, and proposes a simplified model for determination of robust states from data. Sufficient conditions are given under which the global filter is uniformly more robust than all state-specific optimal filters.