The object of the research is non-stationary 1D processes in biomedical systems. The purpose of the dissertation is design of adaptive methods for nonlinear robust filtering of biomedical signals effective in complex conditions of presence of additive non-stationary and additive and multiplicative noises with unknown variances and impulses as well as methods of nonlinear robust filtering for removal of movement artifacts with unknown properties. Methods of research: Theory of nonlinear robust estimates, theory of probability and mathematical statistics, methods of nonlinear robust filtering, Monte-Carlo method, numerical simulation. Theoretical and practical research results: designed methods of locally adaptive robust filtering for processing 1D signals with a priori unknown and different behavior have allowed increasing the efficiency of denoising in conditions of additive non-stationary, additive and multiplicative noises and impulses with small probability, considerable improving accuracy of measuring parameters of triangular and parabolic extrema, providing high efficiency of ECG denoising. The proposed method and the designed adaptive vector nonlinear filter have allowed removing low amplitude artifacts without introducing sufficient distortions of information component, to suppress noise, to preserve changes in signals dealing with periodic events (cycles of ECG, brain evoked potentials). This allowed improving the signal quality for analysis, recognition and classification. Scientific novelty - first the method for removal of low amplitude artifacts in one-lead ECG is proposed that exploits principle of vector nonlinear filtering; this has allowed to automatically remove artifacts in real time without taking into account information on their properties; the method of vector nonlinear filtering has been further advanced, this method, in opposite to existing, the adaptation parameter (statistical criterion for checking suspicious variants) is used for determining the resultant vector, this has allowed to carry out trimming in the case of presence of signals with artifacts in data sample, This provides possibility to eliminate the influence of an artifact on resulting signal, to suppress noise and to preserve eventual changes in signals dealing with events that repeat; the method of locally adaptive robust filtering with hard switching of parameters has been further advanced in the sense of applying nonlinear hybrid filters with extrapolating subapertures as their component, in opposite to existing, this has allowed improving local and integral indicators of filtering efficiency in conditions of additive non-stationary, additive, multiplicative and impulse noise with small probability and to provide high quality of ECG processing; models of nonlinear robust filters have been further advanced in the part of backgrounding their properties that, in opposite to existing, allow selecting the most suitable filter depending upon a given signal-noise situation. Scientific and practical results of the thesis can be used in monitoring systems for high efficiency suppression of non-stationary noise, to remove artifacts with unknown properties in automatic systems of biomedical signal analysis.
