Efficient Denoising of Piecewise-Smooth Signals with Forward-Backward FIR Smoothers

Abstract: A forward-backward (FB) unbiased finite impulse response (UFIR) smoothing algorithm is addressed to provide efficient denoising of piecewise-smooth signals with known or identifiable edge positions. Owing to the time-variant horizon, the algorithm unites advantages of linear structures with robustness of nonlinear ones. The FB UFIR smoother proposed has been examined in Gaussian and heavy-tailed noise environments and compared to the nonlinear myriad filter fitting the Cauchy statistics. Based upon, we show that the smoother is able to preserve edges without jitter and provide denoising with sufficient robustness against outliers.