Hierarchical-likelihood-based wavelet method for denoising signals with missing data

Abstract

This letter proposes a wavelet denoising method in the presence of missing data. This approach is based on a coupling of wavelet shrinkage and hierarchical (or h)-likelihood method. The h-likelihood provides an effective imputation methodology of missing data to give wavelet estimators for signals and motivates a fast and simple algorithm. The method can be easily extended to other settings, such as image denoising. Simulation studies demonstrate empirical properties of the proposed method.