Time-variant forward-backward FIR denoising of piecewise-smooth signals

We address a novel time-variant forward-backward (FB) unbiased finite impulse response (UFIR) smoothing algorithm designed to denoise piecewise-smooth signals with known or well detectable edge positions. Owing to the variable averaging interval, the algorithm unites advantages of linear structures with robustness of nonlinear ones. The FB UFIR smoother has been examined in Gaussian and heavy-tailed noise environments and compared to the nonlinear myriad filter derived under the Cauchy statistics. We show that the solution proposed is able to preserve edges without jitter and provide efficient denoising with sufficient robustness against outliers and noise heavy tails.