Наталия Олеговна Тулякова, Роман Юрьевич Лопаткин, Александр Николаевич Трофимчук, Александр Евгеньевич Стрижак


Local adaptive algorithms of myriad filtering with adaptation of a sample myriad linearity parameter K depending upon local estimates of signal scale and "hard" switching of parameters of sliding window lengths and coefficients that influence on parameter K are proposed. Statistical estimates of filters quality are obtained using criterion of minimum mean-square error for a complex model of one-dimensional signal that includes elementary signals such as a constant signal, step edge, piecewise linear fragments, linearly increasing and decreasing signals, a peak-like maximum, a piecewise function that consists of constant signal and polynomial curve, a parabolic maximum under conditions of additive Gaussian noise with zero mean and different variances and possible spikes presence. It is shown that the proposed myriad locally-adaptive filters can preserve fragments of rapid changing of signal as step edge and other discontinues due to high dynamic properties in nonlinear mode of myriad filtering and small length of the sliding window and can effectively suppress noise while processing fragments of linear signal behavior and polynomial curves by adjusting the parameter K to a linear mode and increasing the window length. Having high efficiency for all fragments of the complex signal, one of the proposed algorithms provides practically optimal noise suppression at the fragment of linear change of the signal, the other one provides higher quality of step-like and constant signals processing. As a result of application of the proposed myriad locally-adaptive filters, improvement of integral and local performance indicators is shown in comparison to the high effective non-linear locally adaptive algorithm that adaptively switches the output signals between median filter with small window length and alpha-trimmed filters with middle and large windows and local-adaptive myriad algorithm with adaptation of the linearity parameter K which are used for the considered test complex signal. Due to the use of multithreading in programing for parallel calculations, all the considered nonlinear algorithms have possibility to be implemented in real time. The more appropriate algorithm for calculating a sample myriad is the algorithm of minimization of myriad cost function based on a numerical Newton technique because of its best performance in step-like signal fragments and best robustness. In order to ensure better spike removal, it is expedient to pre-process the signal by robust myriad filter.


myriad filtering; nonlinear locally adaptive filters; complex one-dimensional signal model; minimum mean square error criterion; statistical estimates of efficiency


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