Noise power spectral density estimation based on optimal smoothing and minimum statistics

TLDR

The paper proposes a method to estimate the power spectral density of nonstationary noise from a noisy speech signal. The approach recursively smooths the noisy speech PSD by minimizing a conditional MSE criterion, tracks spectral minima per frequency band without a voice activity detector, and uses these minima statistics to produce an unbiased noise PSD estimate that can be integrated into any speech enhancement algorithm. The estimator is suitable for real‑time use and demonstrates effective performance in speech enhancement and low‑bit‑rate coding across multiple noise environments.

Abstract

We describe a method to estimate the power spectral density of nonstationary noise when a noisy speech signal is given. The method can be combined with any speech enhancement algorithm which requires a noise power spectral density estimate. In contrast to other methods, our approach does not use a voice activity detector. Instead it tracks spectral minima in each frequency band without any distinction between speech activity and speech pause. By minimizing a conditional mean square estimation error criterion in each time step we derive the optimal smoothing parameter for recursive smoothing of the power spectral density of the noisy speech signal. Based on the optimally smoothed power spectral density estimate and the analysis of the statistics of spectral minima an unbiased noise estimator is developed. The estimator is well suited for real time implementations. Furthermore, to improve the performance in nonstationary noise we introduce a method to speed up the tracking of the spectral minima. Finally, we evaluate the proposed method in the context of speech enhancement and low bit rate speech coding with various noise types.