Piecewise Smooth Signal Denoising Via Principal Curve Projections

One common problem in signal denoising is that if the signal has a blocky, in other words a piecewise-smooth structure, the denoised signal may suffer from oversmoothed discontinuities or exhibit artifacts very similar to Gibbs phenomenon. In the literature, total variation methods and some modifications on the signal reconstructions based on wavelet coefficients are proposed to overcome these problems. We take a novel approach by introducing principal curve projections as an artifact-free signal denoising filter alternative. The proposed approach leads to a nonparametric denoising algorithm that does not lead to Gibbs effect or so-called staircase type unnatural artifacts in the denoised signal.