# An Efficient Multistage Approach for Blind Source Separation of Noisy Convolutive Speech Mixture

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## Abstract

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## 1. Introduction

#### 1.1. Background

#### 1.2. Contributions

- We propose a novel efficient multistage approach for BSS applications. This method concatenates the hybrid approach. Our proposed hybrid models combine multivariate generalized Gaussian and super-Gaussian source priors.
- Based on the hybrid model, two different schemes are introduced, i.e., first BSS followed by de-noising and second de-noising in the first stage followed by BSS.
- The performance of the proposed multistage hybrid model is evaluated with other multistage BSS methods having single source priors.
- The performance of the proposed models are investigated via extensive simulations in a noisy reverberant environment.

#### 1.3. Organization

## 2. Signal Model

## 3. Proposed Multistage BSS Approach

## 4. Results and Discussion

#### 4.1. Experimental Setup

#### 4.2. Objective Evaluation

#### 4.3. Subjective Evaluation

#### 4.4. Results with Colored Noise

#### 4.5. Energy Distribution of Observed Mixtures

## 5. Performance Evaluation

#### Comparative Analysis of the Proposed Models

## 6. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Gupta, V.; Bhowmick, A.; Chandra, M.; Sharan, S. Speech enhancement using MMSE estimation and spectral subtraction methods. In Proceedings of the 2011 International Conference on Devices and Communications (ICDeCom), Mesra, India, 24–25 February 2011; pp. 1–5. [Google Scholar]
- Souden, M.; Araki, S.; Kinoshita, K.; Nakatani, T.; Sawada, H. A multichannel MMSE-based framework for speech source separation and noise reduction. IEEE Trans. Audio Speech Lang. Process.
**2013**, 21, 1913–1928. [Google Scholar] [CrossRef] - Enzner, G.; Thüne, P. Robust MMSE filtering for single-microphone speech enhancement. In Proceedings of the 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), New Orleans, LA, USA, 5–9 March 2017; pp. 4009–4013. [Google Scholar]
- Fenghua, Z.; Le, Y.; Jian, W.; Qiang, S. Speech signal enhancement through wavelet domain MMSE filtering. In Proceedings of the 2010 International Conference on Computer, Mechatronics, Control and Electronic Engineering, Changchun, China, 24–26 August 2010; Volume 5, pp. 118–121. [Google Scholar]
- Kirubagari, B.; Palanivel, S.; Subathra, N. Speech enhancement using minimum mean square error filter and spectral subtraction filter. In Proceedings of the International Conference on Information Communication and Embedded Systems (ICICES2014), Chennai, India, 27–28 February 2014; pp. 1–7. [Google Scholar]
- Khalil, R.A.; Jones, E.; Babar, M.I.; Jan, T.; Zafar, M.H.; Alhussain, T. Speech emotion recognition using deep learning techniques: A review. IEEE Access
**2019**, 7, 117327–117345. [Google Scholar] [CrossRef] - Khalil, R.; Ashraf, S.; Jan, T.; Jehangir, A.; Khan, J. Enhancement of Speech Signals Using Multiple Statistical Models. Sindh Univ. Res. J. SURJ Sci. Ser.
**2015**, 47, 519–522. [Google Scholar] - Yang, J.; Wang, Z. Blind separation algorithm for speech and noise based on diagonalizing second-order statistics accurately. In Proceedings of the 2010 2nd IEEE International Conference on Information Management and Engineering, Chengdu, China, 16–18 April 2010; pp. 370–373. [Google Scholar]
- Hongyan, L.; Guanglong, R. Blind separation of noisy mixed speech signals based Independent Component Analysis. In Proceedings of the 2010 First International Conference on Pervasive Computing, Signal Processing and Applications, Harbin, China, 17–19 September 2010; pp. 586–589. [Google Scholar]
- Yin, J.; Liu, Z.; Jin, Y.; Peng, D.; Kang, J. Blind Source Separation and Identification for Speech Signals. In Proceedings of the 2017 International Conference on Sensing, Diagnostics, Prognostics and Control (SDPC), Shanghai, China, 16–18 August 2017; pp. 398–402. [Google Scholar]
- Rivet, B.; Girin, L.; Jutten, C. Mixing audiovisual speech processing and blind source separation for the extraction of speech signals from convolutive mixtures. IEEE Trans. Audio Speech Lang. Process.
**2006**, 15, 96–108. [Google Scholar] [CrossRef] - Parikh, D.N.; Anderson, D.V. Blind source separation with perceptual post processing. In Proceedings of the 2011 Digital Signal Processing and Signal Processing Education Meeting (DSP/SPE), Sedona, AZ, USA, 4–7 January 2011; pp. 321–325. [Google Scholar]
- Rahima, H.; Djebari, M.; Mohamed, D. Blind speech enhancement and acoustic noise reduction by SFTF adaptive algorithm. In Proceedings of the 2017 5th International Conference on Electrical Engineering-Boumerdes (ICEE-B), Boumerdes, Algeria, 29–31 October 2017; pp. 1–4. [Google Scholar]
- Fisli, S.; Djendi, M.; Guessoum, A. Modified predator-prey particle swarm optimization based two-channel speech quality enhancement by forward blind source separation. In Proceedings of the 2018 2nd International Conference on Natural Language and Speech Processing (ICNLSP), Algiers, Algeria, 25–26 April 2018; pp. 1–6. [Google Scholar]
- Bendoumia, R.; Djendi, M.; Guessoum, A. New symmetric subband forward algorithm based on simple variable step-sizes for speech enhancement. In Proceedings of the 2017 5th International Conference on Electrical Engineering-Boumerdes (ICEE-B), Boumerdes, Algeria, 29–31 October 2017; pp. 1–6. [Google Scholar]
- Bendoumia, R.; Djendi, M. Speech enhancement using backward adaptive filtering algorithm: Variable step-sizes approaches. In Proceedings of the 2015 3rd International Conference on Control, Engineering & Information Technology (CEIT), Tlemcen, Algeria, 25–27 May 2015; pp. 1–5. [Google Scholar]
- Ghribi, K.; Djendi, M.; Berkani, D. Thresholding wavelet-based forward BSS algorithm for speech enhancement and complexity reduction. In Proceedings of the 2018 2nd International Conference on Natural Language and Speech Processing (ICNLSP), Algiers, Algeria, 25–26 April 2018; pp. 1–6. [Google Scholar]
- Beack, S.K.; Lee, B.; Hahn, M.; Nam, S.H. Blind source separation and Kalman filter-based speech enhancement in a car environment. In Proceedings of the 2004 International Symposium on Intelligent Signal Processing and Communication Systems 2004 (ISPACS 2004), Seoul, Korea, 18–19 November 2004; pp. 520–523. [Google Scholar]
- Wang, Z.Q.; Wang, D. Combining spectral and spatial features for deep learning based blind speaker separation. IEEE/ACM Trans. Audio Speech Lang. Process.
**2018**, 27, 457–468. [Google Scholar] [CrossRef] - Wang, H.; Bi, A.; Xu, P.; Gao, C. Convolutive Blind Source Separation Algorithm Based on Higher Order Statistics. In Proceedings of the 2013 Third International Conference on Intelligent System Design and Engineering Applications, Hong Kong, China, 16–18 January 2013; pp. 487–490. [Google Scholar]
- Abdessamed, B.; Yahia, B.; Mohamed, D. Hands Free Communication Improvement in Airplane by a New Dual RNQ Adaptive Algorithm. In Proceedings of the 2018 International Conference on Electrical Sciences and Technologies in Maghreb (CISTEM), Algiers, Algeria, 28–31 October 2018; pp. 1–4. [Google Scholar]
- Wang, C.; Zhu, X.; Li, X. Interference Suppression Based on Single-channel Blind Source Separation in Weather Radar. In Proceedings of the 2019 International Conference on Meteorology Observations (ICMO), Chengdu, China, 28–31 December 2019; pp. 1–4. [Google Scholar]
- Cmejla, J.; Koldovsky, Z. Multi-channel speech enhancement based on independent vector extraction. In Proceedings of the 2018 16th International Workshop on Acoustic Signal Enhancement (IWAENC), Tokyo, Japan, 17–20 September 2018; pp. 525–529. [Google Scholar]
- Tang, H.; Wang, S. Noisy blind source separation based on adaptive noise removal. In Proceedings of the 10th World Congress on Intelligent Control and Automation, Beijing, China, 6–8 July 2012; pp. 4255–4257. [Google Scholar]
- Routray, A.; Das, N.; Dash, P. Robust preprocessing: Denoising and whitening in the context of blind source separation of instantaneous mixtures. In Proceedings of the 2007 5th IEEE International Conference on Industrial Informatics, Vienna, Austria, 23–27 June 2007; Volume 1, pp. 377–380. [Google Scholar]
- Yang, Y.; Li, Z.; Wang, X.; Zhang, D. Noise source separation based on the blind source separation. In Proceedings of the 2011 Chinese Control and Decision Conference (CCDC), Mianyang, China, 23–25 May 2011; pp. 2236–2240. [Google Scholar]
- Chen, Y. Single channel blind source separation based on nmf and its application to speech enhancement. In Proceedings of the 2017 IEEE 9th International Conference on Communication Software and Networks (ICCSN), Guangzhou, China, 6–8 May 2017; pp. 1066–1069. [Google Scholar]
- Yatabe, K.; Kitamura, D. Time-frequency-masking-based Determined BSS with Application to Sparse IVA. In Proceedings of the ICASSP 2019-2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Brighton, UK, 12–17 May 2019; pp. 715–719. [Google Scholar]
- Schwartz, B.; Gannot, S.; Habets, E.A. Two model-based EM algorithms for blind source separation in noisy environments. IEEE/ACM Trans. Audio Speech Lang. Process.
**2017**, 25, 2209–2222. [Google Scholar] [CrossRef] - Wood, S.U.; Rouat, J. Unsupervised low latency speech enhancement with RT-GCC-NMF. IEEE J. Sel. Top. Signal Process.
**2019**, 13, 332–346. [Google Scholar] [CrossRef] [Green Version] - Kim, T.; Attias, H.T.; Lee, S.Y.; Lee, T.W. Blind source separation exploiting higher-order frequency dependencies. IEEE Trans. Audio Speech Lang. Process.
**2006**, 15, 70–79. [Google Scholar] [CrossRef] - Liang, Y.; Naqvi, S.M.; Wang, W.; Chambers, J.A. Frequency domain blind source separation based on independent vector analysis with a multivariate generalized Gaussian source prior. In Blind Source Separation; Springer: Raleigh, NC, USA, 2014; pp. 131–150. [Google Scholar]
- Rafique, W.; Erateb, S.; Naqvi, S.M.; Dlay, S.S.; Chambers, J.A. Independent vector analysis for source separation using an energy driven mixed Student’s t and super Gaussian source prior. In Proceedings of the 2016 24th European Signal Processing Conference (EUSIPCO), Budapest, Hungary, 29 August–2 September 2016; pp. 858–862. [Google Scholar]
- Khan, J.B.; Jan, T.; Khalil, R.A.; Altalbe, A. Hybrid Source Prior Based Independent Vector Analysis for Blind Separation of Speech Signals. IEEE Access
**2020**, 8, 132871–132881. [Google Scholar] [CrossRef] - Soon, Y.; Koh, S.N.; Yeo, C.K. Noisy speech enhancement using discrete cosine transform. Speech Commun.
**1998**, 24, 249–257. [Google Scholar] [CrossRef] - Ephraim, Y.; Malah, D. Speech enhancement using a minimum-mean square error short-time spectral amplitude estimator. IEEE Trans. Acoust. Speech Signal Process.
**1984**, 32, 1109–1121. [Google Scholar] [CrossRef] [Green Version] - Ephraim, Y.; Malah, D. Speech enhancement using a minimum mean-square error log-spectral amplitude estimator. IEEE Trans. Acoust. Speech Signal Process.
**1985**, 33, 443–445. [Google Scholar] [CrossRef] - Boll, S. Suppression of acoustic noise in speech using spectral subtraction. IEEE Trans. Acoust. Speech Signal Process.
**1979**, 27, 113–120. [Google Scholar] [CrossRef] [Green Version] - McAulay, R.; Malpass, M. Speech enhancement using a soft-decision noise suppression filter. IEEE Trans. Acoust. Speech Signal Process.
**1980**, 28, 137–145. [Google Scholar] [CrossRef] - Kim, T.; Lee, I.; Lee, T.W. Independent vector analysis: Definition and algorithms. In Proceedings of the 2006 Fortieth Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA, 29 October–1 November 2006; pp. 1393–1396. [Google Scholar]
- Garofolo, J.S. TIMIT Acoustic Phonetic Continuous Speech Corpus; Linguistic Data Consortium: Philadelphia, PA, USA, 1993. [Google Scholar]
- Rafique, W.; Naqvi, S.M.; Jackson, P.J.; Chambers, J.A. IVA algorithms using a multivariate student’s t source prior for speech source separation in real room environments. In Proceedings of the 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), South Brisbane, QLD, Australia, 19–24 April 2015; pp. 474–478. [Google Scholar]
- Allen, J.B.; Berkley, D.A. Image method for efficiently simulating small-room acoustics. J. Acoust. Soc. Am.
**1979**, 65, 943–950. [Google Scholar] [CrossRef]

**Figure 3.**Change in SDR for convolutive pink noisy mixture with variable SNR for the first proposed model.

**Figure 4.**Change in SDR for convolutive pink noisy mixture with variable SNR for the 2nd proposed model.

**Figure 5.**Change in SDR for convolutive pink noisy mixture with variable RT for the 1st proposed model.

**Figure 6.**Change in SDR for convolutive pink noisy mixture with variable RT in the 2nd proposed model.

**Figure 9.**(

**a**) Comparison of the two proposed models for ${\widehat{S}}_{1}$ with variable SNR (dB); (

**b**) Comparison of the two proposed models for ${\widehat{S}}_{2}$ with variable SNR (dB).

**Figure 10.**(

**a**) Comparison of the two proposed models for ${\widehat{S}}_{1}$ with variable RT (msec); (

**b**) Comparison of the two proposed models for ${\widehat{S}}_{2}$ with variable RT (msec).

**Table 1.**Average SNR results for the first proposed model shown in Figure 1 with variable SNR for multistage BSS models having different source priors.

Multivariate | Student’s T | Generalized | Proposed Model | |||||
---|---|---|---|---|---|---|---|---|

Gaussian | Distribution | Gaussian | ||||||

SNR | Source Prior [31] | Source Prior [42] | Source Prior [32] | |||||

(dB) | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{1}$ | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{2}$ | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{1}$ | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{2}$ | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{1}$ | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{2}$ | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{1}$ | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{2}$ |

−2 | 10.22 | 6.17 | 8.05 | 4.57 | 10.30 | 6.24 | 10.44 | 6.35 |

0 | 9.58 | 5.36 | 7.49 | 4.18 | 9.73 | 5.39 | 9.83 | 5.41 |

2 | 9.30 | 5.08 | 5.98 | 2.02 | 9.51 | 5.31 | 9.66 | 5.33 |

4 | 8.80 | 3.49 | 5.82 | 1.86 | 8.85 | 5.05 | 9.31 | 5.12 |

6 | 8.75 | 3.38 | 5.57 | 1.14 | 8.81 | 3.48 | 8.84 | 3.57 |

8 | 8.62 | 2.37 | 5.33 | 1.00 | 8.71 | 3.36 | 8.81 | 3.42 |

10 | 8.31 | 2.01 | 5.21 | 0.26 | 8.39 | 2.33 | 8.53 | 2.41 |

**Table 2.**Average RT results for the first proposed model shown in Figure 1 with variable RT for multistage BSS models having different source priors.

Multivariate | Student’s T | Generalized | Proposed Model | |||||
---|---|---|---|---|---|---|---|---|

Gaussian | Distribution | Gaussian | ||||||

RT | Source Prior [31] | Source Prior [42] | Source Prior [32] | |||||

(ms) | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{1}$ | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{2}$ | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{1}$ | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{2}$ | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{1}$ | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{2}$ | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{1}$ | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{2}$ |

40 | 16.10 | 7.47 | 9.64 | 2.27 | 16.29 | 7.56 | 16.37 | 7.68 |

80 | 12.45 | 5.79 | 6.94 | 2.00 | 12.65 | 5.72 | 12.81 | 5.87 |

120 | 7.06 | 3.02 | 5.92 | 1.65 | 7.26 | 3.22 | 7.41 | 3.39 |

160 | 4.49 | 2.11 | 2.88 | 1.04 | 4.63 | 2.63 | 4.83 | 2.85 |

200 | 3.92 | 1.62 | 2.25 | 0.28 | 4.01 | 1.81 | 4.23 | 1.97 |

**Table 3.**Average SNR results for the second proposed model shown in Figure 2 with variable SNR for multistage BSS models having different source priors.

Multivariate | Student’s T | Generalized | Proposed Model | |||||
---|---|---|---|---|---|---|---|---|

Gaussian | Distribution | Gaussian | ||||||

SNR | Source Prior [31] | Source Prior [42] | Source Prior [32] | |||||

(dB) | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{1}$ | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{2}$ | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{1}$ | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{2}$ | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{1}$ | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{2}$ | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{1}$ | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{2}$ |

−2 | 5.76 | 4.48 | 3.79 | 5.39 | 5.81 | 4.67 | 5.87 | 4.51 |

0 | 4.37 | 3.74 | 3.44 | 2.86 | 4.39 | 3.38 | 4.53 | 3.87 |

2 | 3.86 | 3.34 | 3.37 | 2.56 | 3.90 | 2.68 | 3.96 | 3.52 |

4 | 3.45 | 2.83 | 2.80 | 2.13 | 3.57 | 2.41 | 3.61 | 2.85 |

6 | 2.34 | 2.18 | 2.37 | 1.02 | 2.40 | 1.95 | 2.43 | 2.47 |

8 | 1.79 | 1.49 | 1.40 | 0.35 | 1.90 | 1.36 | 2.05 | 1.70 |

10 | 0.70 | 1.19 | 0.63 | 0.11 | 0.81 | 1.22 | 1.02 | 1.45 |

**Table 4.**Average RT results for the second proposed model shown in Figure 2 with variable RT for multistage BSS models having different source priors.

Multivariate | Student’s T | Generalized | Proposed Model | |||||
---|---|---|---|---|---|---|---|---|

Gaussian | Distribution | Gaussian | ||||||

RT | Source Prior [31] | Source Prior [42] | Source Prior [32] | |||||

(ms) | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{1}$ | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{2}$ | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{1}$ | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{2}$ | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{1}$ | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{2}$ | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{1}$ | $\mathbf{\Delta}$ SDR ${\mathit{S}}_{2}$ |

40 | 10.86 | 6.32 | 6.30 | 2.50 | 10.85 | 6.35 | 10.97 | 6.43 |

80 | 2.38 | 2.52 | 4.34 | 2.07 | 4.55 | 2.62 | 4.87 | 3.14 |

120 | 2.11 | 1.81 | 3.23 | 1.97 | 4.09 | 2.12 | 4.29 | 2.53 |

160 | 1.72 | 1.56 | 1.19 | 1.16 | 3.82 | 2.06 | 3.91 | 2.39 |

200 | 1.40 | 1.19 | 1.05 | 0.38 | 2.46 | 1.24 | 2.76 | 1.74 |

**Table 5.**Average MOS results of the subjective evaluation for the first model shown in Figure 1 with variable SNR for multistage BSS models having different source priors.

Multivariate | Student’s T | Generalized | Proposed Model | |||||
---|---|---|---|---|---|---|---|---|

Gaussian | Distribution | Gaussian | ||||||

SNR | Source Prior [31] | Source Prior [42] | Source Prior [32] | |||||

(dB) | MOS for ${\mathit{S}}_{1}$ | MOS for ${\mathit{S}}_{2}$ | MOS for ${\mathit{S}}_{1}$ | MOS for ${\mathit{S}}_{2}$ | MOS for ${\mathit{S}}_{1}$ | MOS for ${\mathit{S}}_{2}$ | MOS for ${\mathit{S}}_{1}$ | MOS for ${\mathit{S}}_{2}$ |

−2 | 1.57 | 1.71 | 1.45 | 1.55 | 1.72 | 1.81 | 2.01 | 1.96 |

0 | 2.13 | 2.37 | 1.98 | 2.15 | 2.45 | 2.62 | 2.83 | 2.77 |

2 | 2.57 | 2.62 | 2.34 | 2.44 | 2.88 | 2.76 | 3.21 | 2.99 |

4 | 3.12 | 2.87 | 2.73 | 2.67 | 3.56 | 3.22 | 3.87 | 3.58 |

6 | 3.95 | 3.25 | 3.46 | 3.11 | 4.17 | 3.49 | 4.21 | 3.67 |

8 | 4.37 | 3.63 | 3.88 | 3.34 | 4.42 | 3.86 | 4.53 | 3.93 |

10 | 4.46 | 4.13 | 4.13 | 3.96 | 4.61 | 4.58 | 4.69 | 4.26 |

**Table 6.**Average MOS results of the subjective evaluation for the first model shown in Figure 1 with variable RT for multistage BSS models having different source priors.

Multivariate | Student’s T | Generalized | Proposed Model | |||||
---|---|---|---|---|---|---|---|---|

Gaussian | Distribution | Gaussian | ||||||

RT | Source Prior [31] | Source Prior [42] | Source Prior [32] | |||||

(ms) | MOS for ${\mathit{S}}_{1}$ | MOS for ${\mathit{S}}_{2}$ | MOS for ${\mathit{S}}_{1}$ | MOS for ${\mathit{S}}_{2}$ | MOS for ${\mathit{S}}_{1}$ | MOS for ${\mathit{S}}_{2}$ | MOS for ${\mathit{S}}_{1}$ | MOS for ${\mathit{S}}_{2}$ |

40 | 3.94 | 4.01 | 3.86 | 3.70 | 4.10 | 4.23 | 4.34 | 4.67 |

80 | 3.72 | 3.79 | 3.52 | 3.39 | 3.94 | 3.86 | 4.21 | 4.18 |

120 | 3.18 | 2.75 | 2.63 | 2.57 | 3.49 | 3.18 | 3.68 | 3.44 |

160 | 2.81 | 2.58 | 2.46 | 2.43 | 2.95 | 2.87 | 3.03 | 2.96 |

200 | 2.34 | 2.25 | 2.17 | 2.08 | 2.46 | 2.37 | 2.58 | 2.47 |

**Table 7.**Average MOS results of the subjective evaluation for the second model shown in Figure 2 with variable SNR for multistage BSS models having different source priors.

Multivariate | Student’s T | Generalized | Proposed Model | |||||
---|---|---|---|---|---|---|---|---|

Gaussian | Distribution | Gaussian | ||||||

SNR | Source Prior [31] | Source Prior [42] | Source Prior [32] | |||||

(dB) | MOS for ${\mathit{S}}_{1}$ | MOS for ${\mathit{S}}_{2}$ | MOS for ${\mathit{S}}_{1}$ | MOS for ${\mathit{S}}_{2}$ | MOS for ${\mathit{S}}_{1}$ | MOS for ${\mathit{S}}_{2}$ | MOS for ${\mathit{S}}_{1}$ | MOS for ${\mathit{S}}_{2}$ |

−2 | 1.23 | 1.27 | 1.07 | 1.24 | 1.37 | 1.30 | 1.55 | 1.48 |

0 | 1.91 | 2.08 | 1.74 | 1.63 | 2.21 | 2.26 | 2.43 | 2.39 |

2 | 2.24 | 2.31 | 1.98 | 1.78 | 2.53 | 2.49 | 2.72 | 2.58 |

4 | 2.81 | 2.67 | 2.46 | 2.27 | 2.98 | 2.81 | 3.15 | 3.04 |

6 | 3.22 | 2.91 | 2.83 | 2.71 | 3.45 | 3.22 | 3.59 | 3.45 |

8 | 3.39 | 3.21 | 2.96 | 2.88 | 3.62 | 3.47 | 3.82 | 3.51 |

10 | 3.54 | 3.45 | 3.20 | 3.13 | 3.79 | 3.55 | 3.92 | 3.68 |

**Table 8.**Average MOS results of the subjective evaluation for the second model shown in Figure 2 with variable RT for multistage BSS models having different source priors.

Multivariate | Student’s T | Generalized | Proposed Model | |||||
---|---|---|---|---|---|---|---|---|

Gaussian | Distribution | Gaussian | ||||||

RT | Source Prior [31] | Source Prior [42] | Source Prior [32] | |||||

(ms) | MOS for ${\mathit{S}}_{1}$ | MOS for ${\mathit{S}}_{2}$ | MOS for ${\mathit{S}}_{1}$ | MOS for ${\mathit{S}}_{2}$ | MOS for ${\mathit{S}}_{1}$ | MOS for ${\mathit{S}}_{2}$ | MOS for ${\mathit{S}}_{1}$ | MOS for ${\mathit{S}}_{2}$ |

40 | 3.39 | 3.52 | 3.43 | 3.51 | 3.61 | 3.55 | 3.89 | 3.63 |

80 | 3.19 | 3.35 | 3.05 | 3.16 | 3.35 | 3.48 | 3.55 | 3.52 |

120 | 2.79 | 2.58 | 2.38 | 2.18 | 2.91 | 2.67 | 3.02 | 2.88 |

160 | 2.51 | 2.35 | 2.23 | 1.92 | 2.73 | 2.46 | 2.95 | 2.54 |

200 | 2.36 | 2.14 | 1.89 | 1.67 | 2.51 | 2.33 | 2.68 | 2.39 |

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## Share and Cite

**MDPI and ACS Style**

Khan, J.B.; Jan, T.; Khalil, R.A.; Saeed, N.; Almutiry, M.
An Efficient Multistage Approach for Blind Source Separation of Noisy Convolutive Speech Mixture. *Appl. Sci.* **2021**, *11*, 5968.
https://doi.org/10.3390/app11135968

**AMA Style**

Khan JB, Jan T, Khalil RA, Saeed N, Almutiry M.
An Efficient Multistage Approach for Blind Source Separation of Noisy Convolutive Speech Mixture. *Applied Sciences*. 2021; 11(13):5968.
https://doi.org/10.3390/app11135968

**Chicago/Turabian Style**

Khan, Junaid Bahadar, Tariqullah Jan, Ruhul Amin Khalil, Nasir Saeed, and Muhannad Almutiry.
2021. "An Efficient Multistage Approach for Blind Source Separation of Noisy Convolutive Speech Mixture" *Applied Sciences* 11, no. 13: 5968.
https://doi.org/10.3390/app11135968