Multichannel nonlinear filters for signal and image restoration

Multichannel nonlinear filtering techniques are becoming increasingly important in signal and image restoration. In general they perform better than using only one channel. Furthermore, nonlinear filters are often better than linear filters at removing noise without distorting signal or image features. The main focus in this dissertation is to develop and compare different classes of nonlinear multichannel filters.; In this dissertation, a new class of nonlinear filters is introduced and analyzed, this filter is referred to as the hybrid (H) filter. These filters are formed by taking a linear combination of both the observation samples in temporal or spatial orders and the sorted observed samples. The extension of the single channel H filters and combination (Ll) filters to the multichannel case is proposed. The definitions of the various filters are presented and compared. In addition, the behavior of these filters is studied for a multichannel signal and image corrupted by zero-mean additive Gaussian noise, additive contaminated Gaussian noise, and impulsive noise. The estimated signal or image is optimum under the criterion of the Mean Square Error (MSE) between the output of the filter and the signal or image being estimated. Experimental results show that the MH and MLl filters produce lower MSE than multichannel linear (Ml) filters and multichannel L-filters (ML) filters.; The development of the rank conditioned rank selection (RCRS) filters for the multichannel case is also presented here. These filters will be referred to as multichannel RCRS or MRCRS filters. Some statistical and deterministic properties of these filters are derived. The Mean Absolute Error (MAE) criteria is used for MRCRS filters. Finally, a number of experimental results are studied and presented here in order to illustrate the performance of these filters.