Noisy time series are typical results of observations or technical measurements. Noise reduction and signál structure saving are contradictory but useful aims. Non-linear time series processing is a way for non-gaussian noise suppression. Many valued algebras enriched by square root are able to realize the operators close to the weighted averages. Fuzzy data processing based on Łukasiewicz algebra [3] with square root satisfies the Lipschitz condition and causes constrained sensitivity of the mapping. The paper presents a fuzzy neural network based on Modus Ponens [1] with fuzzy logic function [6] preprocessing in the hidden layer. AU the fuzzy algorithms were realized in the Matlab systém and in C++. The fuzzy processing is applied to prediction of sunspot numbers. The systematic approach based on filter selection is combined with weight optimization.
One of the useful areas of the 2D image processing is called de-noising. When both original (ideal) and noisy images are available, the quality of de-noising is measurable. Our paper is focused to local 2D image processing using Łukasiewicz algebra with the square root function. The basic operators and functions in given algebra are first defined and then analyzed. The first result of the fuzzy logic function (FLF) analysis is its decomposition and realization as Łukasiewicz network (ŁN) with three types of processing nodes. The second result of FLF decomposition is the decomposed Łukasiewicz network (DŁN) with dyadic preprocessing and two types of processing nodes. The decomposition chain, which begins with FLF and converts it to ŁN and then to DŁN, terminates as Łukasiewicz artificial neural network (\lann) with dyadic preprocessing and only one type of processing node. Then the ŁANN is able to learn its integer weights in the ANN style. We are able to realize a set of individual FLF filters as ŁANN. Their preprocessing strategies are based on the pixel neighborhood, sorted list, Walsh list, and L-estimates. The quality of de-noising can be improved via compromise filtering. Two types of compromise de-noising filters are also realizable as ŁANN. One of them is called constrained referential neural network (CRNN). The other one is called dyadic weight neural network (DWNN). The compromise filters operate with the values from the set of individual filters. Both CRNN and DWNN are able to increase the quality of image processing as demonstrated on the biomedical MR image. All the calculations are realized in the Matlab environment
The image de-noising is a practical application of image processing.
Both linear and nonlinear filters are ušed for the noise reduction. The filters which are realizable in Lukasiewicz algebra with square root were analyzed first and then they were used for the 2D image de-noising. There is a set of quality measures recommended for the evaluation of de-noising quality. In čase of various quality measures we can find the best filter. The Pareto optimality principle and the AIA technique were used for this purpose. The procedures were demonstrated on a set of MRI biomedical images.