Two-stage signal restoration based on a modified median filter

Abstract

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 $L_2$-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.

Keywords:

• covariance penalty
• effective degrees of freedom
• Gaussian mixtures
• generalized Stein'sunbiased risk estimator
• smoothing splines

Acknowledgments

The authors thank the editor, the associate editor, the anonymous referee, and Research Fellow Hsin-Cheng, Huang, Institute of Statistical Science, Academia Sinica, Taipei, Taiwan, for helpful comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Ministry of Science and Technology of Taiwan [NSC 102-2118-M-018-002].