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

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.

A data-driven non-intrusive measure of speech quality and intelligibility

“…is the estimated noise power spectrum obtained by the minimum statistics algorithm [49], [46] and P y (i, k) is the power spectrum of the noisy speech signal.…”

Uncertainty decoding on Frequency Filtered parameters for robust ASR

“…For our experiments, we used γ = 0.8 and β = 0.2. | S| was estimated as an average over the magnitude spectra at the previous, current, and next time frames (Boll (1979)), while | N | was estimated using the minimum statistics method proposed in Martin (2001). In order to estimate the noise power spectrum density, Martin (2001) assumes that each noise power spectrum component follows an Exponential distribution.…”

“…| S| was estimated as an average over the magnitude spectra at the previous, current, and next time frames (Boll (1979)), while | N | was estimated using the minimum statistics method proposed in Martin (2001). In order to estimate the noise power spectrum density, Martin (2001) assumes that each noise power spectrum component follows an Exponential distribution. However, since we were interested in estimating the noise magnitude instead of the noise power spectrum, we used a Rayleigh model, resulting from applying a root square operator on an Exponential variable (Papoulis and Pillai (2002)).…”

The synergy between bounded-distance HMM and spectral subtraction for robust speech recognition

“…For this paper we used the minimum statistics method proposed by Martin (2001) to perform the estimation of the noise power spectral density. Essentially, the method looks for minima in the power spectrum of the contaminated speech signal.…”