Optimization of Threshold Boolean Filters
Ki Dong Lee, Yong Hoon Lee · 2005
Recently, a new class of nonrecursive digital filters, which is called the threshold Boolean filter (TBF), has been introduced as an extension of stack filters. While a procedure for finding a TBF that yields a smaller mean absolute error (MAE) than an optimal stack filter is known, no efficient algorithm for finding the best TBF in the MAE sense is available at this time. As an alternative, the optimal TBF under the mean square error (MSE) criterion is considered in this paper. It is shown that the optimization problem can be formulated into a known problem: the minimization of a pseudo-Boolean quadratic function, which is an NP-hard problem. In this paper, a numerical method embedded in a branch and bound algorithm is adopted to solve the minimization problem. Some computer experiments with real signals are performed, and the results of optimal threshold Boolean filtering are compared with those of linear FIR Wiener and optimal stack filters.