Two-stage binary filters

Filter design involves a trade-off between the size of the filter class ove r which optimization is to be performed and the size of the training sample . As the number of parameters determining the filter class grows, so too do es the size of the training sample required to obtain a given degree of pre cision when estimating the optimal filter from the sample data. A common wa y to moderate the estimation problem is to use a constrained filter requiri ng less parameters, but then a trade-off between the theoretical filter per formance and the estimation precision arises. The overall result strongly d epends on the constraint type. Approaches presented in this paper divide th e filter operation into two stages and apply constraints only to the first stage. Such filters are advantageous since they are fully optimal with resp ect to certain subsets of the filter window. Error expression, representati on, and design methodology are discussed A generic optimization algorithm f or such two-stage filters is proposed. Special attention is paid to three p articular cases, for which properties, design algorithms, and experimental results are provided: two-stage filters with linearly separable preprocessi ng, two-stage filters with restricted window preprocessing. and two-stage i terative filters. (C) 1999 SPIE and IS&T. [S1017-9909(99)00603-0].