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的局部自适应滤波方法。研究目标为：针对先验信息有限（仅掌握信号模型与噪声方差的少量先验知识）、且信息分量行为模式存在差异的信号，开发一种可抑制非平稳噪声（以其时变方差为核心特征）的局部自适应算法。需完成的研究任务包括：一是针对包含多种基础信号、且加性高斯噪声方差波动范围较广的一维复杂过程模型，通过处理质量的数值统计估计，验证所提局部自适应myriad滤波器 (myriad filter) 的降噪有效性；二是针对模型信号与实际采集信号，探究非平稳噪声抑制的实际效果。研究方法如下：通过数值仿真（蒙特卡洛 (Monte Carlo) 分析），基于均方误差 (mean square error) 准则，构建滤波器质量的全局与局部评价指标。所得研究结果如下：提出了一种适配噪声与信号的myriad滤波器，可针对信息分量行为模式各异、噪声方差显著波动的信号，实现非平稳噪声抑制。经数值仿真得到的滤波器质量统计估计结果表明，相较于其他高性能局部自适应算法，所提局部自适应myriad滤波器在不同噪声水平下均具备更优的降噪效率。实验验证表明，该滤波器可在极低噪声水平下几乎完整保留原始信号，在低、中噪声水平下的滤波动态误差极小，且在高噪声方差场景下具备更出色的噪声抑制能力。对输出信号、局部自适应参数曲线及可调参数的分析结果，证实了所研究的局部自适应算法具备高效性与运行正确性。此类非线性滤波器展现出优异的鲁棒性，同时证实了将原有鲁棒汉普尔滤波器 (Hampel filter) 中的中值运算替换为myriad运算以实现尖峰消除的合理性。本文还给出了眼震电图 (electronystagmogram) 信号中实现高质量非平稳噪声抑制的应用实例。结论 本研究所得结果的科学创新性在于：开发了一类具备时变噪声与信号依赖参数的局部自适应myriad滤波器，可用于处理信号行为与噪声方差均为非平稳的降噪场景。该算法无需额外耗时进行滤波器参数自适应调整与精确校准，亦无需信号模型与噪声方差的先验知识，可应用于准实时处理场景。所提出的适配噪声与信号的myriad滤波器，可在噪声非平稳性（方差波动）显著的复杂场景下，有效提升信号处理的质量。