Weighted median autoregressive graph filters

The graph filter can extract the desired features from the graph signal and filter out the noise signal. Most of the graph filters proposed in the literature are linear. Autoregressive moving average (ARMA) filter is a polynomial filter. Compared to finite-impulse response (FIR) graph filters, ARMA graph filters are robust to changes in the signal and/or graph, but are still linear. In this work, we propose a weighted median autoregressive graph filter (WMAF) based on a first-order ARMA graph filter. The proposed filter is a combination of weighted median filter in the traditional signal processing field and median autoregressive filters (MAF), and can be implemented in a distributed way. Compared with linear filter and MAF, the proposed WMAF filter has better filtering effect on pulse noise. In the denoising application of real sensor network data set, the filtered signal has a better signal-to-noise ratio.