A new linear MMSE filter for single channel speech enhancement based on Nonnegative Matrix Factorization

Single channel speech enhancement using Bayesian NMF with recursive temporal updates of prior distributions

“…We assume that the magnitude spectrogram of the noisy speech signal is approximated by the sum of the speech and noise magnitude spectrograms, i.e., |y.τ | ≈ |s.τ | + |n.τ |. Note that although this assumption is not theoretically well justified, it is a common assumption in NMF based speech processing [1,2,4,5,6], and has led to good results in practice. Let us denote the number of the basis vectors for speech as I and for noise as J; the first line of (1) is now written as:…”

“…NMF has been used in a variety of applications in audio processing including, but not limited to, blind source separation [1,2,3] and speech enhancement [4,5,6]. For these applications, the magnitude (or power) spectrogram of the speech signal, X, is factorized into its basis matrix T and a time-varying NMF coefficients matrix V , such that: X ≈ T V .…”

“…In our previous work [6], a linear MMSE filter was proposed to enhance the noisy speech; though, no explicit prior density function was assumed for the parameters of interest. In this paper, we explicitly assign a prior distribution, in the form of a Gamma density function, to the NMF coefficients.…”

A Survey on Techniques for Enhancing Speech

“…(1) Supervised methods (like NMF, HMM) where noise and speech are modeled according to training samples [13]. [2].…”

Non-negative Tensor Factorization for Speech Enhancement

“…first proposed a NMF based speech enhancement algorithm and obtained good results [7]. Mohammadiha and et.al. put forward this idea in several ways, for example the design of filter model, the study of NMF constraint condition and the comparison of supervised and unsupervised methods, and further proved the effectiveness of the NMF in the field of speech enhancement [8][9] [10]. In spite of these improvement, they still take vectors as inputs.…”