Adaptive ASR Filtering in Impulsive Noise Environments

In the field of impulsive noise processing based on alpha-stable distribution model, the classical filtering methods have been largely motivated by special cases of alpha-stable family such as Cauchy distribution and Meridian distribution, and their pulse suppression ability is limited. To address the above limitations, a class of robust cost functions are devised and a robust filtering method ASR (${\rm{AS}}\alpha {\rm{S}} $ kobust) is proposed, based on the M estimation theory and the $ {\rm{AS}}\alpha {\rm{S}} $ distribution model, with its robustness analyzed by the influence functions. Then the expression of the linearity parameter is proposed and a threshold selection method is adopted for an adaptive linearity parameter selection. The unified theoretical framework of robust filtering is devised, and Myriad filters and Meridian filters are interpreted within the unifying framework. In addition, a filtering method which is, namely AS-FT (ASR STFT) is developed and the parameters estimation of noisy Linear Frequency Modulation (LFM) signals shows the robustness of ASR filtering. Simulation results show that the ASR method is more robust to outliers than Myriad filters, Median filters, fractional lower-order statistics and other traditional robust filters.