Iterative robust peak-aware guided filter for signal smoothing

Due to the imperfection of experimental measurements, the measured spectrum signals are inevitably corrupted by random error (noise). It is very useful in applications to remove the noise in the measured data while preserving some significant features (such as peaks) by a smoothing filtering process. This paper presents a peak-preserving smoothing technique in the framework of guided filtering for spectrum signals, called robust peak-aware guided filter (RPAGF). Firstly, the robust peak-aware weight (RPAW) is introduced by means of hyperbolic tangent with threshold parameter, where the parameter is estimated by the median of absolute deviations from the median of local variances of the signal under consideration. Then the RPAGF is presented by incorporating the RPAW of a guidance signal into the cost function of guided filter as the regularization coefficient. The RPAGF uses the Gaussian-weighted averaging to deal with the problem of overlapping windows involved in computing filtering output, while the guidance signal is generated by a time fractional diffusion filtering from the input signal. Finally, the self-iteration scheme of RPAGF called iterative RPAGF (IRPAGF) is designed to provide a more faithful guidance signal for RPAGF at each iteration. The IRPAGF is evaluated by experiments on simulated and real spectrum signals, in comparison to the relevant state-of-the-art methods. Results show that the IRPAGF achieves higher performance in terms of peak-preserving smoothing of spectrum signals.