Variational mode decomposition denoising combined the detrended fluctuation analysis

Abstract

A novel signal denoising method that combines variational mode decomposition (VMD) and detrended fluctuation analysis (DFA), named DFA–VMD, is proposed in this paper. VMD is a recently introduced technique for adaptive signal decomposition, which is theoretically well founded and more robust to sampling and noise compared with empirical mode decomposition (EMD). The noisy signal is first broken down into a given number K band-limited intrinsic mode functions (BLIMFs) by VMD. Then a simple criterion based on DFA is designed to select the number K, aiming to avoid the impact of overbinning or underbinning on the VMD denoising. In addition, DFA is also developed to define the relevant modes to construct the filtered signal. After that, the computational complexity of DFA–VMD denoising is analyzed, and its time complexity is equivalent to the EMD. Experimental results, on simulated and real signals, show the superior performance of this proposed filtering over EMD-based denoisings and discrete wavelet threshold filtering.