Locally-adaptive Myriad Filtration of One-dimensional Complex Signal

Abstract

Locally-adaptive algorithms of myriad filtering are proposed with adaptation of a sample myriad linearity parameter K, depending upon local estimates of a signal, and with “hard” switching of sliding window length settings and a coefficient which influences on the parameter K. Statistical estimates of the filters quality are obtained using a criterion of a minimum mean-square error for a model of one-dimensional complex signal that includes different elementary segments under conditions of additive Gaussian noise with zero mean and different variances and possible spikes presence. Improvement of integral and local performance indicators is shown in comparison to the highly effective non-linear locally-adaptive algorithms for the considered test signal. Having a complex signal of high efficiency, one of the proposed algorithms provides nearly optimal noise suppression at the segments of linear change of a signal; other algorithm provides higher quality of step edge preservation and the best noise suppression on a const signal. Better efficiency in cases of low and high noise levels is achieved by preliminary noise level estimation through comparison of locally-adaptive parameter and thresholds. It is shown that, in order to ensure better spikes removal, it is expedient to pre-process the signal by robust myriad filter with small window length. The considered adaptive nonlinear filters have possibility to be implemented in a real time mode.

Keywords

• Locally-adaptive myriad filtering
• One-dimensional complex signals
• Minimum mean square error criterion
• Statistical estimates of filter efficiency