Adaptive ASR Filtering in Impulsive Noise Environments
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摘要: 在基于alpha稳定分布模型的脉冲噪声处理领域中，经典滤波方法多采用Cauchy分布和Meridian分布等alpha稳定分布特例，其脉冲抑制能力有限。对此，该文基于M估计理论和
$ {\rm{AS}}\alpha {\rm{S}} $ 分布模型，构造稳健滤波代价函数簇，提出ASR稳健滤波方法，利用影响函数分析其稳健性，构建稳健滤波的统一理论基础，将Myriad滤波，Meridian滤波统一起来。给出线性度参数表达式，并采用阈值选择法实现自适应选择。此外，提出AS-FT滤波方法，以线性调频(LFM)信号在脉冲噪声下的参数估计为例，表明ASR滤波方法的稳健性。仿真实验表明，ASR稳健滤波方法，与中值滤波、Myriad滤波、分数低阶等传统的稳健滤波方法相比，具有良好的鲁棒性。Abstract: 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.-
Key words:
- ASαS distribution /
- Cost function /
- Influence function /
- Robust filtering
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表 1 常用滤波器的代价函数与影响函数
均值滤波 中值滤波 Myriad滤波 Meridian滤波 PDF $p(x)$ ${{\exp ( - {x^2})} / {\sqrt {2\pi } }}$ ${ {\exp ( - \left| x \right|)} / {2\pi } }$ ${\gamma / {[\pi ({\gamma ^2} + {x^2})]}}$ ${{\delta / {2(\delta + \left| x \right|}}^2})$ 代价函数 $F(e)$ ${e^2}$ $\left| e \right|$ $\log ({e^2} + {\gamma ^2})$ $\log \{ \delta + \left| e \right|\} $ 影响函数 $\varphi (e)$ $2e$ ${\rm{sgn}} (e)$ $2e/({\gamma ^2} + {e^2})$ ${\rm{sgn}} (e)/(\delta + |e|)$ 
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