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2014 | OriginalPaper | Chapter

12. On the Ideal Ratio Mask as the Goal of Computational Auditory Scene Analysis

Authors : Christopher Hummersone, Toby Stokes, Tim Brookes

Published in: Blind Source Separation

Publisher: Springer Berlin Heidelberg

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Abstract

The ideal binary mask (IBM) is widely considered to be the benchmark for time–frequency-based sound source separation techniques such as computational auditory scene analysis (CASA). However, it is well known that binary masking introduces objectionable distortion, especially musical noise. This can make binary masking unsuitable for sound source separation applications where the output is auditioned. It has been suggested that soft masking reduces musical noise and leads to a higher quality output. A previously defined soft mask, the ideal ratio mask (IRM), is found to have similar properties to the IBM, may correspond more closely to auditory processes, and offers additional computational advantages. Consequently, the IRM is proposed as the goal of CASA. To further support this position, a number of studies are reviewed that show soft masks to provide superior performance to the IBM in applications such as automatic speech recognition and speech intelligibility. A brief empirical study provides additional evidence demonstrating the objective and perceptual superiority of the IRM over the IBM.

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Literature
1.
go back to reference Anzalone, M., Calandruccio, L., Doherty, K., Carney, L.: Determination of the potential benefit of time-frequency gain manipulation. Ear and hearing 27(5), 480 (2006)CrossRef Anzalone, M., Calandruccio, L., Doherty, K., Carney, L.: Determination of the potential benefit of time-frequency gain manipulation. Ear and hearing 27(5), 480 (2006)CrossRef
2.
go back to reference Araki, S., Makino, S., Sawada, H., Mukai, R.: Underdetermined blind separation of convolutive mixtures of speech with directivity pattern based mask and ICA. In: Puntonet, C., Prieto, A. (eds.) Independent Component Analysis and Blind Signal Separation. Lecture Notes in Computer Science, vol. 3195, pp. 898–905. Springer, Berlin (2004) Araki, S., Makino, S., Sawada, H., Mukai, R.: Underdetermined blind separation of convolutive mixtures of speech with directivity pattern based mask and ICA. In: Puntonet, C., Prieto, A. (eds.) Independent Component Analysis and Blind Signal Separation. Lecture Notes in Computer Science, vol. 3195, pp. 898–905. Springer, Berlin (2004)
3.
go back to reference Araki, S., Makino, S., Sawada, H., Mukai, R.: Reducing musical noise by a fine-shift overlap-add method applied to source separation using a time-frequency mask. IEEE Int. Conf. Acoust. Speech Signal Proc. (ICASSP) III, 81–84 (2005) Araki, S., Makino, S., Sawada, H., Mukai, R.: Reducing musical noise by a fine-shift overlap-add method applied to source separation using a time-frequency mask. IEEE Int. Conf. Acoust. Speech Signal Proc. (ICASSP) III, 81–84 (2005)
4.
go back to reference Araki, S., Nesta, F., Vincent, E., Koldovsk, Z., Nolte, G., Ziehe, A., Benichoux, A.: The 2011 signal separation evaluation campaign (SiSEC2011): audio source separation. In: Theis, F., Cichocki, A., Yeredor, A., Zibulevsky, M. (eds.) Latent Variable Analysis and Signal Separation. Lecture Notes in Computer Science, vol. 7191, pp. 414–422. Springer, Berlin, Heidelberg (2012) Araki, S., Nesta, F., Vincent, E., Koldovsk, Z., Nolte, G., Ziehe, A., Benichoux, A.: The 2011 signal separation evaluation campaign (SiSEC2011): audio source separation. In: Theis, F., Cichocki, A., Yeredor, A., Zibulevsky, M. (eds.) Latent Variable Analysis and Signal Separation. Lecture Notes in Computer Science, vol. 7191, pp. 414–422. Springer, Berlin, Heidelberg (2012)
5.
go back to reference Araki, S., Sawada, H., Mukai, R., Makino, S.: Blind sparse source separation with spatially smoothed time-frequency masking. In: International Workshop on Acoustic, Echo and Noise Control. Paris (2006) Araki, S., Sawada, H., Mukai, R., Makino, S.: Blind sparse source separation with spatially smoothed time-frequency masking. In: International Workshop on Acoustic, Echo and Noise Control. Paris (2006)
6.
go back to reference Barker, J., Josifovski, L., Cooke, M.P., Green, P.D.: Soft decisions in missing data techniques for robust automatic speech recognition. In: Proceedings of International Conference on Spoken Language Processing, pp. 373–376 (2000) Barker, J., Josifovski, L., Cooke, M.P., Green, P.D.: Soft decisions in missing data techniques for robust automatic speech recognition. In: Proceedings of International Conference on Spoken Language Processing, pp. 373–376 (2000)
7.
go back to reference Bell, A.J., Sejnowski, T.J.: An information-maximization approach to blind separation and blind deconvolution. Neural computation 7(6), 1129–1159 (1995)CrossRef Bell, A.J., Sejnowski, T.J.: An information-maximization approach to blind separation and blind deconvolution. Neural computation 7(6), 1129–1159 (1995)CrossRef
8.
go back to reference Bregman, A.: The meaning of duplex perception: sounds as transparent objects. In: Schouten, M.E.H. (ed.) The Psychophysics of Speech Perception, pp. 95–111. Martinus Nijhoff, Dordrecht (1987) Bregman, A.: The meaning of duplex perception: sounds as transparent objects. In: Schouten, M.E.H. (ed.) The Psychophysics of Speech Perception, pp. 95–111. Martinus Nijhoff, Dordrecht (1987)
9.
go back to reference Bregman, A.S.: Auditory Scene Analysis. MIT Press, Cambridge (1990) Bregman, A.S.: Auditory Scene Analysis. MIT Press, Cambridge (1990)
10.
go back to reference Brons, I., Houben, R., Dreschler, W.A.: Perceptual effects of noise reduction by time-frequency masking of noisy speech. J. Acoust. Soc. Am. 132(4), 2690–2699 (2012)CrossRef Brons, I., Houben, R., Dreschler, W.A.: Perceptual effects of noise reduction by time-frequency masking of noisy speech. J. Acoust. Soc. Am. 132(4), 2690–2699 (2012)CrossRef
11.
go back to reference Brungart, D.S., Chang, P.S., Simpson, B.D., Wang, D.: Isolating the energetic component of speech-on-speech masking with ideal time-frequency segregation. J. Acoust. Soc. Am. 120(6), 4007–4018 (2006)CrossRef Brungart, D.S., Chang, P.S., Simpson, B.D., Wang, D.: Isolating the energetic component of speech-on-speech masking with ideal time-frequency segregation. J. Acoust. Soc. Am. 120(6), 4007–4018 (2006)CrossRef
12.
go back to reference Christensen, H., Barker, J., Ma, N., Green, P.: The chime corpus: a resource and a challenge for computational hearing in multisource environments. In: Proceedings of Interspeech (2010) Christensen, H., Barker, J., Ma, N., Green, P.: The chime corpus: a resource and a challenge for computational hearing in multisource environments. In: Proceedings of Interspeech (2010)
13.
go back to reference Coy, A., Barker, J.: An automatic speech recognition system based on the scene analysis account of auditory perception. Speech Commun. 49(5), 384–401 (2007)CrossRef Coy, A., Barker, J.: An automatic speech recognition system based on the scene analysis account of auditory perception. Speech Commun. 49(5), 384–401 (2007)CrossRef
14.
go back to reference Emiya, V., Vincent, E., Harlander, N., Hohmann, V.: Subjective and objective quality assessment of audio source separation. IEEE Trans. Audio Speech Lang. Proc. 19(7), 2046–2057 (2011) Emiya, V., Vincent, E., Harlander, N., Hohmann, V.: Subjective and objective quality assessment of audio source separation. IEEE Trans. Audio Speech Lang. Proc. 19(7), 2046–2057 (2011)
15.
go back to reference Ephraim, Y., Malah, D.: Speech enhancement using a minimum-mean square error short-time spectral amplitude estimator. IEEE Trans. Acoust. Speech Signal Proc. 32(6), 1109–1121 (1984) Ephraim, Y., Malah, D.: Speech enhancement using a minimum-mean square error short-time spectral amplitude estimator. IEEE Trans. Acoust. Speech Signal Proc. 32(6), 1109–1121 (1984)
16.
go back to reference Ephraim, Y., Malah, D.: Speech enhancement using a minimum mean-square error log-spectral amplitude estimator. IEEE Trans. Acoust. Speech Signal Proc. 33(2), 443–445 (1985) Ephraim, Y., Malah, D.: Speech enhancement using a minimum mean-square error log-spectral amplitude estimator. IEEE Trans. Acoust. Speech Signal Proc. 33(2), 443–445 (1985)
17.
go back to reference Erkelens, J., Hendriks, R., Heusdens, R., Jensen, J.: Minimum mean-square error estimation of discrete fourier coefficients with generalized gamma priors. IEEE Trans. Audio Speech Lang. Proc. 15(6), 1741–1752 (2007) Erkelens, J., Hendriks, R., Heusdens, R., Jensen, J.: Minimum mean-square error estimation of discrete fourier coefficients with generalized gamma priors. IEEE Trans. Audio Speech Lang. Proc. 15(6), 1741–1752 (2007)
18.
go back to reference Grais, E., Erdogan, H.: Single channel speech music separation using nonnegative matrix factorization and spectral masks. In: The 17th International Conference on Digital Signal Processing, pp. 1–6 (2011) Grais, E., Erdogan, H.: Single channel speech music separation using nonnegative matrix factorization and spectral masks. In: The 17th International Conference on Digital Signal Processing, pp. 1–6 (2011)
19.
go back to reference Hartmann, W., Fosler-Lussier, E.: Investigations into the incorporation of the ideal binary mask in ASR. In: IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), pp. 4804–4807 (2011) Hartmann, W., Fosler-Lussier, E.: Investigations into the incorporation of the ideal binary mask in ASR. In: IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), pp. 4804–4807 (2011)
20.
go back to reference Hendriks, R., Heusdens, R., Jensen, J.: MMSE based noise PSD tracking with low complexity. In: IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), pp. 4266–4269 (2010) Hendriks, R., Heusdens, R., Jensen, J.: MMSE based noise PSD tracking with low complexity. In: IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), pp. 4266–4269 (2010)
21.
go back to reference Hu, Y., Loizou, P.C.: Techniques for estimating the ideal binary mask. In: Proceedings 11th International Workshop on Acoustic Echo and Noise Control (2008) Hu, Y., Loizou, P.C.: Techniques for estimating the ideal binary mask. In: Proceedings 11th International Workshop on Acoustic Echo and Noise Control (2008)
22.
go back to reference Jensen, J., Hendriks, R.: Spectral magnitude minimum mean-square error estimation using binary and continuous gain functions. IEEE Trans. Audio Speech Lang. Proc. 20(1), 92–102 (2012) Jensen, J., Hendriks, R.: Spectral magnitude minimum mean-square error estimation using binary and continuous gain functions. IEEE Trans. Audio Speech Lang. Proc. 20(1), 92–102 (2012)
23.
go back to reference Jutten, C., Hérault, J.: Independent component analysis (inca) versus principal component analysis. In: Signal Processing IV: Theories and applications—Proceedings of EUSIPCO, pp. 643–646. North-Holland, Grenoble (1988) Jutten, C., Hérault, J.: Independent component analysis (inca) versus principal component analysis. In: Signal Processing IV: Theories and applications—Proceedings of EUSIPCO, pp. 643–646. North-Holland, Grenoble (1988)
24.
go back to reference Lee, D.D., Seung, H.S.: Learning the parts of objects by non-negative matrix factorization. Nature 401(6755), 788–791 (1999)CrossRef Lee, D.D., Seung, H.S.: Learning the parts of objects by non-negative matrix factorization. Nature 401(6755), 788–791 (1999)CrossRef
25.
go back to reference Li, M., McAllister, H., Black, N., De Perez, T.: Perceptual time-frequency subtraction algorithm for noise reduction in hearing aids. IEEE Trans. Biomed. Eng. 48(9), 979–988 (2001)CrossRef Li, M., McAllister, H., Black, N., De Perez, T.: Perceptual time-frequency subtraction algorithm for noise reduction in hearing aids. IEEE Trans. Biomed. Eng. 48(9), 979–988 (2001)CrossRef
26.
go back to reference Li, N., Loizou, P.C.: Effect of spectral resolution on the intelligibility of ideal binary masked speech. J. Acoust. Soc. Am. 123(4), 59–64 (2008)CrossRef Li, N., Loizou, P.C.: Effect of spectral resolution on the intelligibility of ideal binary masked speech. J. Acoust. Soc. Am. 123(4), 59–64 (2008)CrossRef
27.
go back to reference Li, N., Loizou, P.C.: Factors influencing intelligibility of ideal binary-masked speech: implications for noise reduction. J. Acoust. Soc. Am. 123(3), 1673–1682 (2008)CrossRef Li, N., Loizou, P.C.: Factors influencing intelligibility of ideal binary-masked speech: implications for noise reduction. J. Acoust. Soc. Am. 123(3), 1673–1682 (2008)CrossRef
28.
go back to reference Li, Y., Wang, D.: On the optimality of ideal binary time-frequency masks. Speech Commun. 51(3), 230–239 (2009)CrossRef Li, Y., Wang, D.: On the optimality of ideal binary time-frequency masks. Speech Commun. 51(3), 230–239 (2009)CrossRef
29.
go back to reference Madhu, N., Breithaupt, C., Martin, R.: Temporal smoothing of spectral masks in the cepstral domain for speech separation. In: IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 45–48 (2008) Madhu, N., Breithaupt, C., Martin, R.: Temporal smoothing of spectral masks in the cepstral domain for speech separation. In: IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 45–48 (2008)
30.
go back to reference Madhu, N., Spriet, A., Jansen, S., Koning, R., Wouters, J.: The potential for speech intelligibility improvement using the ideal binary mask and the ideal Wiener filter in single channel noise reduction systems: Application to auditory prostheses. IEEE Trans. Audio Speech Lang. Proc. 21(1), 63–72 (2013) Madhu, N., Spriet, A., Jansen, S., Koning, R., Wouters, J.: The potential for speech intelligibility improvement using the ideal binary mask and the ideal Wiener filter in single channel noise reduction systems: Application to auditory prostheses. IEEE Trans. Audio Speech Lang. Proc. 21(1), 63–72 (2013)
31.
go back to reference Makkiabadi, B., Sanei, S., Marshall, D.: A k-subspace based tensor factorization approach for under-determined blind identification. In: Forty Fourth Asilomar Conference on Signals, Systems and Computers, pp. 18–22 (2010) Makkiabadi, B., Sanei, S., Marshall, D.: A k-subspace based tensor factorization approach for under-determined blind identification. In: Forty Fourth Asilomar Conference on Signals, Systems and Computers, pp. 18–22 (2010)
32.
go back to reference Moore, B.C.J.: An Introduction to the Psychology of Hearing, 5th edn. Academic Press, London (2004) Moore, B.C.J.: An Introduction to the Psychology of Hearing, 5th edn. Academic Press, London (2004)
33.
go back to reference Mowlaee, P., Saeidi, R., Martin, R.: Model-driven speech enhancement for multisource reverberant environment (signal separation evaluation campaign (SiSEC) 2011). In: Theis, F., Cichocki, A., Yeredor, A., Zibulevsky, M. (eds.) Latent Variable Analysis and Signal Separation. Lecture Notes in Computer Science, vol. 7191, pp. 454–461. Springer, Berlin, Heidelberg (2012) Mowlaee, P., Saeidi, R., Martin, R.: Model-driven speech enhancement for multisource reverberant environment (signal separation evaluation campaign (SiSEC) 2011). In: Theis, F., Cichocki, A., Yeredor, A., Zibulevsky, M. (eds.) Latent Variable Analysis and Signal Separation. Lecture Notes in Computer Science, vol. 7191, pp. 454–461. Springer, Berlin, Heidelberg (2012)
34.
go back to reference Naik, G.R., Kumar, D.K.: An overview of independent component analysis and its applications. Informatica 35, 63–81 (2011)MATH Naik, G.R., Kumar, D.K.: An overview of independent component analysis and its applications. Informatica 35, 63–81 (2011)MATH
35.
go back to reference Ozerov, A., Vincent, E., Bimbot, F.: A general flexible framework for the handling of prior information in audio source separation. IEEE Trans. Audio Speech Lang. Proc. 20(4), 1118–1133 (2012) Ozerov, A., Vincent, E., Bimbot, F.: A general flexible framework for the handling of prior information in audio source separation. IEEE Trans. Audio Speech Lang. Proc. 20(4), 1118–1133 (2012)
36.
go back to reference Patterson, R., Nimmo-Smith, I., Holdsworth, J., Rice, P.: An efficient auditory filterbank based on the gammatone function. Technical report, MRC Applied Psychology Unit, Cambridge (1987) Patterson, R., Nimmo-Smith, I., Holdsworth, J., Rice, P.: An efficient auditory filterbank based on the gammatone function. Technical report, MRC Applied Psychology Unit, Cambridge (1987)
37.
go back to reference Pedersen, M., Wang, D., Larsen, J., Kjems, U.: Overcomplete blind source separation by combining ICA and binary time-frequency masking. In: IEEE Workshop Machine Learning Signal Processing, pp. 15–20 (2005) Pedersen, M., Wang, D., Larsen, J., Kjems, U.: Overcomplete blind source separation by combining ICA and binary time-frequency masking. In: IEEE Workshop Machine Learning Signal Processing, pp. 15–20 (2005)
38.
go back to reference Peterson, W., Birdsall, T.G., Fox, W.C.: The theory of signal detectability. In: Proceedings of the IRE Professional Group on Information Theory 4, pp. 171–212 (1954) Peterson, W., Birdsall, T.G., Fox, W.C.: The theory of signal detectability. In: Proceedings of the IRE Professional Group on Information Theory 4, pp. 171–212 (1954)
39.
go back to reference Rangachari, S., Loizou, P.C.: A noise-estimation algorithm for highly non-stationary environments. Speech Commun. 48(2), 220–231 (2006)CrossRef Rangachari, S., Loizou, P.C.: A noise-estimation algorithm for highly non-stationary environments. Speech Commun. 48(2), 220–231 (2006)CrossRef
40.
go back to reference Roman, N., Wang, D.: Pitch-based monaural segregation of reverberant speech. J. Acoust. Soc. Am. 120(1), 458–469 (2006)CrossRef Roman, N., Wang, D.: Pitch-based monaural segregation of reverberant speech. J. Acoust. Soc. Am. 120(1), 458–469 (2006)CrossRef
41.
go back to reference Shannon, R., Zeng, F., Kamath, V., Wygonski, J., Ekelid, M.: Speech recognition with primarily temporal cues. Science 270, 303–303 (1995)CrossRef Shannon, R., Zeng, F., Kamath, V., Wygonski, J., Ekelid, M.: Speech recognition with primarily temporal cues. Science 270, 303–303 (1995)CrossRef
42.
go back to reference Srinivasan, S., Roman, N., Wang, D.: Binary and ratio time-frequency masks for robust speech recognition. Speech Commun. 48(11), 1486–1501 (2006)CrossRef Srinivasan, S., Roman, N., Wang, D.: Binary and ratio time-frequency masks for robust speech recognition. Speech Commun. 48(11), 1486–1501 (2006)CrossRef
43.
go back to reference Stokes, T., Hummersone, C., Brookes, T.: Reducing binary masking artefacts in blind audio source separation. In: Proceedings of 134th Engineering Society Convention Rome (2013) Stokes, T., Hummersone, C., Brookes, T.: Reducing binary masking artefacts in blind audio source separation. In: Proceedings of 134th Engineering Society Convention Rome (2013)
44.
go back to reference Swets, J.A.: Is there a sensory threshold? Science 134(3473), 168–177 (1961)CrossRef Swets, J.A.: Is there a sensory threshold? Science 134(3473), 168–177 (1961)CrossRef
45.
go back to reference Swets, J.A.: Signal Detection and Recognition by Human Observers. Wiley, New York (1964) Swets, J.A.: Signal Detection and Recognition by Human Observers. Wiley, New York (1964)
46.
go back to reference Tanner Jr, W.P., Swets, J.A.: A decision-making theory of visual detection. Psychol. Rev. 61(6), 401–409 (1954)CrossRef Tanner Jr, W.P., Swets, J.A.: A decision-making theory of visual detection. Psychol. Rev. 61(6), 401–409 (1954)CrossRef
47.
go back to reference Vincent, E., Gribonval, R., Févotte, C.: Performance measurement in blind audio source separation. IEEE Trans. Audio Speech Lang. Proc. 14(4), 1462–1469 (2006) Vincent, E., Gribonval, R., Févotte, C.: Performance measurement in blind audio source separation. IEEE Trans. Audio Speech Lang. Proc. 14(4), 1462–1469 (2006)
48.
go back to reference Wang, D.: On ideal binary mask as the computational goal of auditory scene analysis. In: Divenyi, P. (ed.) Speech Separation by Humans and Machines, pp. 181–197. Kluwer Academic, Norwell (2005) Wang, D.: On ideal binary mask as the computational goal of auditory scene analysis. In: Divenyi, P. (ed.) Speech Separation by Humans and Machines, pp. 181–197. Kluwer Academic, Norwell (2005)
49.
go back to reference Wang, D.: Time-frequency masking for speech separation and its potential for hearing aid design. Trends Amplif. 12(4), 332–353 (2008)CrossRef Wang, D.: Time-frequency masking for speech separation and its potential for hearing aid design. Trends Amplif. 12(4), 332–353 (2008)CrossRef
50.
go back to reference Wang, D., Brown, G.J.: Fundamentals of computational auditory scene analysis. In: Wang, D., Brown, G.J. (eds.) Computational Auditory Scene Analysis: Principles, Algorithms and Applications, pp. 1–44. Wiley, Hoboken (2006) Wang, D., Brown, G.J.: Fundamentals of computational auditory scene analysis. In: Wang, D., Brown, G.J. (eds.) Computational Auditory Scene Analysis: Principles, Algorithms and Applications, pp. 1–44. Wiley, Hoboken (2006)
51.
go back to reference Wiener, N.: Extrapolation, Interpolation, and Smoothing of Stationary Time Series: with Engineering Applications. MIT Press, Cambridge (1950) Wiener, N.: Extrapolation, Interpolation, and Smoothing of Stationary Time Series: with Engineering Applications. MIT Press, Cambridge (1950)
Metadata
Title
On the Ideal Ratio Mask as the Goal of Computational Auditory Scene Analysis
Authors
Christopher Hummersone
Toby Stokes
Tim Brookes
Copyright Year
2014
Publisher
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-642-55016-4_12