Variational Mode Decomposition Denoising Using Anderson-Darling Statistics

A novel signal denoising method is proposed based on variational mode decomposition (VMD) and Anderson-Darling statistics. The VMD method expands a signal into its frequency components, i.e., time series corresponding to a narrow range frequencies, termed intrinsic mode functions (IMFs) of the input signal. While initial IMFs contain most of the signal, the challenge remains the identification of these IMFs and presence of noise in the IMFs corresponding to signal. We propose to address this problem using the Anderson-Darling (AD) test. To that end, we compare the empirical distribution function (EDF) of the local coefficients of the VMD with the EDF of noise using AD statistics under the framework of goodness-of-fit (GoF) test. The coefficients exhibiting noise-like distribution are set to zero for noise removal. We demonstrate the effectiveness of proposed VMD-AD-GoF method using simulations on wide variety of signals.