Design of threshold Boolean filters under MSE criterion by iterative searching

Threshold Boolean filters (TBFs) constitute a large class of nonlinear filters which are effective in removing impulsive noise and preserving image details. The minimum mean square error (MMSE) design of TBFs is found to be a quadratic 0-1 programming problem. Unfortunately, solving the problem needs a huge number of computations. We propose an iterative search algorithm of very low complexity to solve the design problem sub-optimally. In each iteration, only one variable is considered and updated. Simulation shows that the proposed algorithm converges quickly and often converges to the optimal solution.