Fast sub-optimal design of extended threshold Boolean filters

Extended threshold Boolean filters (ETBFs) constitute a large class of nonlinear filters that include the threshold Boolean filters (TBFs) and linear FIR filters. The minimum mean square error (MMSE) design of ETBFs is however of high (computational) complexity. In this paper, we introduce two new design methods for sub-optimal ETBFs, with much lower complexity. The methods try to minimize the sum of micro or state MSEs (instead of the actual MSE). The resulting filters are applied to enhance noisy images, and the simulations show that the performance is very close to that of the MMSE design.