For many years, linear filters have been the dominant class of filters in signal processing because of their sound theoretical background. However, not all signal processing problems can be satisfactorily solved by linear filters. On the contrary, nonlinear filters often perform better than linear filters in many applications. For instance, in noisy image processing, linear filters fail to suppress impulsive noise effectively and they tend to blur sharp edges which carry important information. But median filter, a nonlinear filter, can suppress impulsive noise effectively and preserve edges....[ Read more ]

For many years, linear filters have been the dominant class of filters in signal processing because of their sound theoretical background. However, not all signal processing problems can be satisfactorily solved by linear filters. On the contrary, nonlinear filters often perform better than linear filters in many applications. For instance, in noisy image processing, linear filters fail to suppress impulsive noise effectively and they tend to blur sharp edges which carry important information. But median filter, a nonlinear filter, can suppress impulsive noise effectively and preserve edges.

A large class of nonlinear filters which includes median filter is called the extended threshold Boolean filters (ETBF's ). They are effective in suppressing noise and preserving edges and details.

In this thesis, ETBF's and their sub-classes are reviewed. Their formulations, properties, and design methods are discussed. In particular, the minimum mean square error (MMSE) design of ETBF's and one of its sub-class, the threshold Boolean filters (TBF's ), are found to have high complexity. Fast algorithms are proposed to approximate the optimal solutions. The performances of the filters designed by these methods are close to those of the optimal ones.

New nonlinear filters, referred to as the reduced threshold Boolean filters (RTBF's ), are proposed. Based on the binary vectors obatined in a filter window, a RTBF selects a sample in the window as output. Despite their simple operations, RTBF's perform closely to TBF's whose complexity is high.

Other applications of these threshold-type filters in image processing are exploited. For instance, in edge detection and prediction, threshold-type flters are found to have better performance and be more robust than linear filters.