ADAPTIVE MYRIAD FILTER WITH TIME-VARYING NOISE- AND SIGNAL-DEPENDENT PARAMETERS

The research subject of the 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 a priori information about a signal model and noise variance. The tasks to be solved 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 which contains different elementary signals in a wide range of additive Gaussian noise variance variation; 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 suppression of non-stationary noise with significantly varying variance in signals with different behavior 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 algorithms. 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 for spike elimination the previous robust Hampel filter in which the median operation is replaced by a myriad one. Examples of signals displaying the high quality of non-stationary noise suppression in an 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 algorithm does not require time for filter parameters adaptation and their exact adjustment, a priori knowledge of the signal model and noise variance, and can be applied in quasi-real-time mode. The proposed noise- and signal-adapting myriad filter improves the quality of signal processing in difficult conditions of significant noise non-stationarity (variance variation).

本文的研究主题为非平稳信号局部自适应滤波的方法。研究目标在于开发一种针对非平稳噪声（从其时间变异性方差的角度出发）的局部自适应算法，该算法针对具有不同行为的信息成分的信号，并限制了对信号模型和噪声方差的先验信息。待解决的问题包括：研究所提出的局部自适应多重滤波器在包含广泛范围加性高斯噪声方差变化的不同基本信号的复杂一维过程中的处理质量数值统计估计的有效性；研究非平稳噪声抑制在模型和真实信号中的有效性。研究方法包括：根据均方误差准则，通过数值模拟（蒙特卡洛分析）获得了积分和局部滤波器质量指标。以下结果是：针对具有不同行为的信息成分的信号，其中噪声方差显著变化，提出了一种噪声和信号自适应的多重滤波器以抑制非平稳噪声。通过数值模拟评估的滤波器质量统计估计显示出，与其它高效局部自适应算法相比，所提出的局部自适应多重滤波器在噪声水平不同的条件下具有更高的效率。在极低噪声水平下实现了信号的近乎完全保留，在低和中等噪声水平下的滤波引起的动态误差最小化，以及在噪声方差较高值下的更有效的噪声抑制。输出信号的分析和局部自适应及自适应参数的参数图证实了所研究的局部自适应算法的高效性和正确操作。展示了这些非线性滤波器的高鲁棒特性，以及使用先前稳健的Hampel滤波器（其中中值操作被多重操作替代）进行尖峰消除的实用性。展示了显示非平稳噪声抑制在眼震图中的高质量信号的例子。结论。所获得结果的科学新颖性在于开发了具有时间变异性噪声和信号相关参数的局部自适应多重滤波器，用于非平稳信号行为和噪声方差的去噪过程。此算法无需为滤波器参数的适应和精确调整、信号模型和噪声方差的前知以及可以在准实时模式下应用。所提出的噪声和信号自适应多重滤波器在显著噪声非平稳（方差变化）的困难条件下改善了信号处理质量。