Threshold decomposition based-locally adaptive linear filters

This paper introduces a filter class which generalizes the extended threshold Boolean filter (ETBF) to encompass many other classes of linear and nonlinear filters. The proposed filter uses two observation windows and it can be described as a locally adaptive linear filter. One window (usually the largest) collects the inputs of the linear filter while the threshold decomposition of the other one is used to compute the weights. As in the case of ETBF, the new filter possesses an MSE-optimal design similar to linear filters. An efficient iterative design algorithm is developed for the proposed filter which also applies for ETBF. Experimental results show that the new method can provide better filtering performance than ETBF.