Адаптивний міріадний фільтр із шумо- та сигнально-залежним зміненням параметрів у часі

Abstract

The research subject of this article is the methods of locally adaptive filtering of non-stationary signals. The goal is to develop a locally-adaptive algorithm for non-stationary noise (from the viewpoint of its time-varying variance) suppression in signals characterized by a different behavior of the informative component, with restricted apriori information about the signal model and noise variance. The tasks are to investigate the effectiveness of the proposed local-adaptive myriad filter using numerical statistical estimates of processing quality for a complex model of one-dimensional process that contains different elementary signals in various additive Gaussian noise variance variations; to investigate the effectiveness of non-stationary noise suppression for model and real signals. The methods are integral and local indicators of filter quality according to the criteria of the mean square error have been obtained using numerical simulation (via Monte Carlo analysis). The following results have been obtained: a noise- and signal-adapting myriad filter for the suppressing of non-stationary noise with significantly varying variance in signals with different behaviors of the informative component is proposed. Statistical estimates of the filter quality, evaluated by numerical simulation, show a higher efficiency of the proposed local-adaptive myriad filter in conditions of different noise levels compared to the other highly efficient locally-adaptive filters. Practically, total preservation of a signal at very low noise levels, minimal dynamical errors caused by filtering at low and middle noise levels, and more effective noise suppression at high values of noise variance are demonstrated. The analysis of output signals and plots of parameters for local adaptation and adaptable parameters confirm the high efficiency and correct operation of the investigated locally-adaptive algorithms. The high robust properties of these nonlinear filters are shown, as well as the expedience of using to spike the elimination of the previous robust Hampel filter in which the median operation is replaced by a myriad one. Examples displaying the high quality of non-stationary noise suppression in a biomedical signal of electronystagmogram are presented. Conclusions. The scientific novelty of the obtained results is the development of locally-adaptive myriad filters with time-varying noise- and signal-dependent parameters for de-noising processes with non-stationary signal behavior and noise variance. This filter does not require time for parameter adaptation and their exact adjustment, a priori knowledge of the signal model and noise variance, and can be applied in a quasi-real-time mode. The proposed algorithm of noise- and signal-adapting myriad filtering algorithm improves the quality of signal processing in difficult conditions of significant noise non-stationarity (variance variation).