Online Parametric NMF for Speech Enhancement

Abstract

In this paper, we propose a speech enhancement method based on non-negative matrix factorization (NMF) techniques. NMF techniques allow us to approximate the power spectral density (PSD) of the noisy signal as a weighted linear combination of trained speech and noise basis vectors arranged as the columns of a matrix. In this work, we propose to use basis vectors that are parameterised by autoregressive (AR) coefficients. Parametric representation of the spectral basis is beneficial as it can encompass the signal characteristics like, e.g. the speech production model. It is observed that the parametric representation of basis vectors is beneficial while performing online speech enhancement in low delay scenarios.

A Novel NMF-HMM Speech Enhancement Algorithm Based on Poisson Mixture Model

“…To evaluate the performance of the proposed method, we compare to two state-of-the-art methods, namely the NMF-HMM [24] and the variable span linear filters [6] (SLF-NMF) combined with parametric NMF [10] for estimating the noise and speech statsitics.…”

“…Therefore, the supervised speech enhancement method have been proposed like NMF [9]. Among the supervised speech enhancement algorithms, the codebook-driven auto-regressive (AR) model based method [10], the auto-regressive hidden Markov model (ARHMM) method [11] and non-negative matrix factorization (NMF) based methods [12] are noteworthy methods. These algorithms can make good use of prior information about both speech and noise, and, as a result, they can often achieve better speech enhancement performance than the unsupervised methods, particularly in non-stationary acoustic environments.…”

Hearing Aid-controlled Beamformer for Binaural Speech Enhancement Using a Model-based Approach

“…Once the speech codebook is created, the spectral envelopes corresponding to the AR coefficients ({au} U u=1 ) are computed and arranged as columns of the spectral basis matrix D as explained by (4) and (5). Given the observed data and the spectral basis matrix D, it has been shown in [7,13] that the maximum likelihood estimation of the activation coefficients corresponds to minimising the IS divergence between the periodogram of the observed signal and the modelled PSD. Since there is no closed form solution for this, it is generally estimated iteratively using the multiplicative update (MU) rule [14] aŝ…”

“…In this work, we propose a model-based method to estimate the direction of arrival via a collaboration between the HA and the external device. We use a model that we proposed in a previous paper [7] to represent the signal received at the HA as well as the external device. The estimated model parameters are subsequently used to estimate the direction of arrival by measuring the similarity between the model parameters.…”

Adaptive Pre-whitening Based on Parametric NMF

“…In a similar way, we here investigate if an adaptive pre-whitener (i.e., whose parameters change every time frame) based on offline trained speech and noise spectral envelopes can render the noise closer to white, and thereby improve the estimation accuracy of a maximum likelihood (ML) pitch estimator [12], [13]. Specifically, a sum of AR processes model [14] is considered, which was motivated by the source/filter speech production model. In this model, the likelihood maximization corresponds to a parametric non-negative matrix factorization (NMF) [15] of the observed periodogram matrix into a dictionary matrix of pretrained spectral envelopes, parametrized by AR coefficients, and a matrix of activation coefficients, with the Itakura-Saito (IS) divergence as the optimization criterion.…”