Two-stage signal restoration based on a modified median filter

Median filter is a robust technique for signal restoration when outliers occurred within observations. Moreover, smoothing splines is also an alternative method for recovering the underlying signals. Interestingly, we found that neither median filter nor smoothing splines dominates each other. To obtain a more robust signal estimate, a two-stage procedure for signal denoising is considered, in which the smoothing spline method is applied again to capture possible information within the differences of median filter and smoothing spline estimates. Then, according to an approximate estimator of (Formula presented.) -risk, a modified median filter method is proposed to estimate the underlying signals. Various comparisons are made via simulation studies to illustrate the superiority of the proposed method.