# An Efficient Multistage Approach for Blind Source Separation of Noisy Convolutive Speech Mixture
###### Abstract  
This paper proposes a novel efficient multistage algorithm to extract source speech signals from a noisy convolutive mixture. The proposed approach comprises two stages named Blind Source Separation (BSS) and de-noising. A hybrid source prior model separates the source signals from the noisy reverberant mixture in the BSS stage. Moreover, we model the low- and high-energy components by generalized multivariate Gaussian and super-Gaussian models, respectively. We use Minimum Mean Square Error (MMSE) to reduce noise in the noisy convolutive mixture signal in the de-noising stage. Furthermore, the two proposed models investigate the performance gain. In the first model, the speech signal is separated from the observed noisy convolutive mixture in the BSS stage, followed by suppression of noise in the estimated source signals in the de-noising module. In the second approach, the noise is reduced using the MMSE filtering technique in the received noisy convolutive mixture at the de-noising stage, followed by separation of source signals from the de-noised reverberant mixture at the BSS stage. We evaluate the performance of the proposed scheme in terms of signal-to-distortion ratio (SDR) with respect to other well-known multistage BSS methods. The results show the superior performance of the proposed algorithm over the other state-of-the-art methods. blind source separation (BSS); minimum mean square error (MMSE); convolutive mixture; source prior; generalized Gaussian distribution +
Footnote †: journal: Applied  
_Article_  
An Efficient Multistage Approach for Blind Source Separation of Noisy Convolutive Speech Mixture  
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Then, the matrices' diagonalization can be exploited accurately by computing a generalized singular value decomposition (GSVD) using the tangent algorithm [8]. The BSS methods extract the desired source speech signal from the convolutive mixture in the presence of noise. Various BSS methods such as Independent Component Analysis (ICA) and FASTICA extract the source speech signals in a noisy reverberant environment. First, the ICA de-noises the noisy reverberant mixture followed by the FASTICA algorithm to separate the de-noised estimated speech signal from the observed convolutive mixture [9]. Additionally, in an undermined scenario, ICA is combined with a speech recognition system (SRS) to extract the desired targeted speech signal [10]. However, these methods require prior knowledge of the mixing process and a number of source signals. Therefore, the advantage of our proposed BSS methods is that it separates the targeted source speech signal from the reverberant mixture without prior knowledge of the mixing process nor the number of source signals. This gives our approach an additional efficiency over existing speech processing methods that require prior knowledge or training. Unlike the existing models, we have used multivariate generalized Gaussian and super-Gaussian source priors as a hybrid source prior model. In this hybrid model, the generalized Gaussian source prior exploits higher-order statistical properties while multivariate super-Gaussian models use other related information. The main problem encountered by BSS techniques is the permutation and scaling ambiguities after the speech separation process. Therefore, in [11], the authors proposed a solution that can easily recognize the desired source speech signal in a noisy environment by looking at the speaker's face. An audiovisual coherence is used to estimate the speech signals using statistical methods where statistical tools model the audio and visual information in the frequency domain (FD). Furthermore, in multiple audio sources with scenarios with multiple microphones, the performance of the BSS separation process is improved by using the BSS output to generate the Wiener filter coefficients and applying them to the desired speech signals [12]. Moreover, adaptive filtering with BSS can also reduce the noise, leading to speech enhancement and noise reduction.