Design and Analysis of Robust Binary Filters in the Context of a Prior Distribution for the States of Nature

Authors:
Artyom M. Grigoryan;Edward R. Dougherty
Affiliations:
Department of Electrical Engineering and Texas Center for Applied Technology, Texas A&M University, College Station, TX;Department of Electrical Engineering and Texas Center for Applied Technology, Texas A&M University, College Station, TX
Venue:
Journal of Mathematical Imaging and Vision
Year:
1999

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Abstract

An optimal binary-image filter estimates an ideal randomset by means of an observed random set. A fundamental and practicallyimportant question regards the robustness of a designed filter: towhat extent does performance degrade when the filter is applied to adifferent model than the one for which it has been designed? Byparameterizing the ideal and observation random sets, one can analyzethe robustness of filter design relative to parameter states. Basedon a prior distribution for the states, a robustness mesure isdefined for each state in terms of how well its optimal filterperforms on models for different states. Not only is filterperformance on other states taken into account, but so too is thecontribution of other states in terms of their mass relative to theprior state distribution. This paper characterizes maximally robuststates, derives performance bounds, treats mean robustness (asopposed to robustness by state), introduces a global filter that isapplied across all states, particularizes the entire analysis to asparse noise model for which there are analytic robustnessexpressions, and proposes a simplified model for determination ofrobust states from data. Sufficient conditions are given under whichthe global filter is uniformly more robust than all state-specificoptimal filters.