Multivariate Denoising and Missing Data Estimation for Heavy-Tailed Signals

Abstract

This study focuses on heavy-tailed noise reduction in multivariate signals, with no knowledge of their forms. We propose a non-parametric multivariate denoising technique which is robust to heavy-tailed noise. Using a univariate robust linear regression, we construct a multivariate non-parametric method. We design a robust matrix decomposition and, consequently, propose a robust procedure including this new decomposition. In addition, we develop a robust procedure for the imputation of the missing points of the signals. The key advantage of our methods over the previous tools is the robustness to the heavy-tailed observations. The results of our simulation study confirm the good performance of the proposed methods.