| In this dissertation, the author illustrates the concept of partitioning the observation space to build a general class of filters referred to as partition-based (P) filters. The structure of P filters consists of two main parts; the partitioning and the associated filtering function. Each observation vector is mapped to a certain partition and each partition has an associated filtering function. Also introduced and analyzed in this dissertation are three new partitioning schemes; one partitioning scheme is based on vector quantization, another partitioning scheme is based on the local mean of the observation vector, and the third partitioning scheme is based on scalar quantization. The proposed partitioning schemes and the resulting filters can track various signal nonstationarities. Adaptive approaches for computing the optimum P filter parameters are introduced and developed. The proposed filters can be applied to one-dimensional or multidimensional signals including those involving Gaussian/non-Gaussian processes. Simulations include a novel approach to estimating response-to-response variations in evoked potentials (EP) buried in the on-going electroencephalogram, frequency selective estimation of a corrupted chirp signal, and Markov signal and image restorations. Experimental results show that the proposed filters produce lower mean-squared error than many well-known filters. |
