Phase-Aware Single-Channel Speech Enhancement With Modulation-Domain Kalman Filtering

Abstract

Abstract-We present a speech enhancement algorithm that performs modulation-domain Kalman filtering to track the speech phase using circular statistics, along with the log-spectra of speech and noise. In the proposed algorithm, the speech phase posterior is used to create an enhanced speech phase spectrum for the signal reconstruction of speech. The Kalman filter prediction step separately models the temporal inter-frame correlation of the speech and noise spectral log-amplitudes and of the speech phase, while the Kalman filter update step models their nonlinear relations under the assumption that speech and noise add in the complex short-time Fourier transform domain. The phasesensitive enhancement algorithm is evaluated with speech quality and intelligibility metrics, using a variety of noise types over a range of SNRs. Instrumental measures predict that tracking the speech log-spectrum and phase with modulation-domain Kalman filtering leads to consistent improvements in speech quality, over both conventional enhancement algorithms and other algorithms that perform modulation-domain Kalman filtering.

Speech Enhancement Using Kalman Filtering in the Logarithmic Bark Power Spectral Domain

“…The phase factor in STFT bins, ↵ k , is given by ↵ k = cos( (k) (k)), as in [9], [7] and [8]. For clarity, we omit the time-frame index, t, below and we only include it in equations involving multiple frames.…”

“…As shown in Fig. 1, decorrelation is performed before the KF update using B 2 < (p+q)⇥(p+q) , as in [8] and [3]. Decorrelation and recorrelation are performed before and after the nonlinear KF update step, respectively.…”

“…In (8), the outer integration over the phase factor in Bark bands, l , is performed using G sigma points. E{ z l }, as computed in Sec.…”

“…We approximate the posterior of the speech and noise spectral log-powers as a two-dimensional Gaussian distribution with a full covariance matrix using the probability distribution of the phase factor in Bark bands. The phasesensitive KF update step computes the first two moments of the posterior distribution, [8], [7], [9], suppressing noise.…”

Modulation-Domain Kalman Filtering for Monaural Blind Speech Denoising and Dereverberation

“…This approach was extended in [10] to use an improved signal model in which speech and noise were additive in the complex STFT domain rather than in the spectral amplitude domain. This was further developed in [52] to minimise the squared error in the logspectral domain and to track the speech phase in addition to the speech and noise amplitudes. Non-linear KFs that take into account that speech and noise add in the STFT domain are formulated in [53], [54] and [11].…”