Enhancement of white Gaussian noise affected speech using VMD-ℓ 1 trend filter method

Abstract

In this paper, a two step approach using Variational Mode Decomposition (VMD) and ℓ₁ trend filter is proposed for enhancing speech signals degraded by white Gaussian noise. In the first step, VMD decomposes the noisy speech signal into Intrinsic Mode Functions (IMFs) corresponding to different frequency components of the signal. In the second step, ℓ₁ trend filter retrieves the speech information by filtering out the noisy sub frames. The noisy sub frames are identified using a threshold based on noise variance in the corresponding IMFs. The proposed work experiments on speech signals degraded by white Gaussian noise in the range 10 dB– 30 dB. The performance of proposed method is compared with some of the well known speech enhancement techniques: Spectral Subtraction (SS) and Minimized Mean Square Error (MMSE) using the subjective and objective quality measures. The proposed, two-step approach of VMD-ℓ₁ trend filter achieves better performance compared to the considered methods.