A forward-backward UFIR algorithm for denoising of piecewise-smooth signals

A new time-variant forward-backward (FB) unbiased finite impulse response (UFIR) smoothing algorithm is addressed to denoise piecewise signals with known or well detectable breakpoints. The algorithm unites advantages of linear structures with robustness of the nonlinear ones. The FB UFIR smoother has been examined in Gaussian and Cauchy noise environments in a comparison to the myriad filter. It is shown that the solution proposed preserves edges without jitter, provides efficient denoising, and is sufficiently robust against the heavy-tailed noise.