Enhancement of variational mode decomposition with missing values

This paper considers an improvement of variational mode decomposition (VMD) in the presence of missing values. VMD developed by Dragomiretskiy and Zosso (2014) efficiently decomposes a signal into some meaningful modes according to their frequency information. It is well known that VMD is useful for tone detection and denoising of noisy signals. However, VMD may not be efficient for analyzing missing data since it is based on discrete Fourier transform (DFT). This paper proposes a new VMD procedure that can effectively handle problems caused by missing values. The proposed method is based on an estimation of spectral density that reflects frequency information of a signal properly with removing the effects of missing samples; hence, it is able to produce stable decomposition results. Results from numerical studies including simulation study and real data analysis demonstrate the promising empirical properties of the proposed method.