Abstract
When speech signals are captured in real acoustical environments, the captured signals are distorted by certain types of interference, such as ambient noise, reverberation, and extraneous speakers’ utterances. There are two important approaches to speech enhancement that reduce such interference in the captured signals. One approach is based on the spatial features of the signals, such as direction of arrival and acoustic transfer functions, and enhances speech using multichannel audio signal processing. The other approach is based on speech spectral models that represent the probability density function of the speech spectra, and it enhances speech by distinguishing between speech and noise based on the spectral models. In this chapter, we propose a new approach that integrates the above two approaches. The proposed approach uses the spatial and spectral features of signals in a complementary manner to achieve reliable and accurate speech enhancement. The approach can be applied to various speech enhancement problems, including denoising, dereverberation, and blind source separation (BSS). In particular, in this chapter, we focus on applying the approach to BSS. We show experimentally that the proposed integration can improve the performance of BSS compared with a conventional approach.
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Notes
- 1.
As noted later, despite this assumption, this scenario can represent a situation with long reverberation, and can be used for achieving dereverberation.
- 2.
If we interpret the ATFs from s t to \(z_{t}^{(m)}\) also as a part of the interference, we may formulate speech enhancement that estimates s t . This is beyond the scope of this chapter.
- 3.
The same model can be used to represent ambient noise, for example, as in [10]. The way to formulate MLSE for denoising and its extension to MAPSE can be found in [12]. As regards MLSE based dereverberation with the long-term linear prediction approach, the generative model of the interference can be defined in the following form [10, 11, 16].
$$\displaystyle\begin{array}{rcl} p(\mathbf{a}_{n,f}\vert \theta _{f})& =& \delta (\mathbf{a}_{n,f} -\mathbf{r}_{n,f}(\theta _{f})), {}\end{array}$$(9.16)where δ(⋅ ) is the Dirac delta function, and \(\mathbf{r}_{n,f}(\theta _{f}) = [r_{n,f}^{(1)}(\theta _{f}),r_{n,f}^{(2)}(\theta _{f}),\ldots,r_{n,f}^{(M)}(\theta _{f})]^{T}\) is a spatial vector of the interference signal, namely the late reverberation signal. The model parameter set θ f is composed of the prediction coefficients, and the late reverberation \(r_{n,f}^{(m)}(\theta _{f})\) is modeled by an inner product of a vector containing the prediction coefficients and that containing a past captured signal in the MLSE based dereverberation. It was shown that the MLSE based dereverberation can be extended to MAPSE based dereverberation as discussed in [11] based on the technique discussed in this chapter.
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Iwata, Y., Nakatani, T., Yoshioka, T., Fujimoto, M., Saito, H. (2015). Maximum A Posteriori Spectral Estimation with Source Log-Spectral Priors for Multichannel Speech Enhancement. In: Ogunfunmi, T., Togneri, R., Narasimha, M. (eds) Speech and Audio Processing for Coding, Enhancement and Recognition. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1456-2_9
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