Abstract
In this article, we propose a new source separation method in which the dual-tree complex wavelet transform (DTCWT) and short-time Fourier transform (STFT) algorithms are used sequentially as dual transforms and sparse nonnegative matrix factorization (SNMF) is used to factorize the magnitude spectrum. STFT-based source separation faces issues related to time and frequency resolution because it cannot exactly determine which frequencies exist at what time. Discrete wavelet transform (DWT)-based source separation faces a time-variation-related problem (i.e., a small shift in the time-domain signal causes significant variation in the energy of the wavelet coefficients). To address these issues, we utilize the DTCWT, which comprises two-level trees with different sets of filters and provides additional information for analysis and approximate shift invariance; these properties enable the perfect reconstruction of the time-domain signal. Thus, the time-domain signal is transformed into a set of subband signals in which low- and high-frequency components are isolated. Next, each subband is passed through the STFT and a complex spectrogram is constructed. Then, SNMF is applied to decompose the magnitude part into a weighted linear combination of the trained basis vectors for both sources. Finally, the estimated signals can be obtained through a subband binary ratio mask by applying the inverse STFT (ISTFT) and the inverse DTCWT (IDTCWT). The proposed method is examined on speech separation tasks utilizing the GRID audiovisual and TIMIT corpora. The experimental findings indicate that the proposed approach outperforms the existing methods.
Similar content being viewed by others
Data availability
The datasets generated or analyzed during the current study are not publicly available because they are the subject of ongoing research but are available from the first author upon reasonable request.
References
G. Bao, Y. Xu, Z. Ye, Learning a discriminative dictionary for single-channel speech separation. IEEE Trans. Audio Speech Lang. Process. 22(7), 1130–1138 (2014)
M. Cooke, J. Barker, S. Cunningham, X. Shao, An audio-visual corpus for speech perception and automatic speech recognition. J. Acoust. Soc. Am. 120(5), 2421 (2006)
D.L. Daniel, H.S. Seung, Learning the pans of objects with non-negative matrix factorization. Nature 401, 788–791 (1999)
M.G. Emad, E. Hakan, Single channel speech music separation using nonnegative matrix factorization with sliding windows and spectral masks. Digital Signal Processing (DSP), in 17th International Conference in August (2011)
G.G. Francois, J.M. Gautham, Stopping criteria for non-negative matrix factorization based supervised and semi-supervised source separation. IEEE Signal Processing Letters, November (2014)
J. Garofolo, et al., TIMIT acoustic-phonetic continuous speech corpus. LDC93S1 (1993)
E.M. Grais, H. Erdogan, Discriminative non-negative dictionary learning using cross-coherence penalties for single channel source separation, in Proceedings of the International Conference on Spoken Language Processing (INTERSPEECH). Lyon, France, 25–29 August (2013)
R. Hidayat, A. Bejo, S. Sumaryono, A. Winursito, Denoising speech for MFCC feature extraction using wavelet transformation in speech recognition system, in 10th International Conference on Information Technology and Electrical Engineering (2018)
P.O. Hoyer, Non-negative matrix factorization with sparseness constraint. J. Mach. Learn. Res. 1457–1469, November (2004)
Y. Hu, P.C. Loizou, Evaluation of objective quality measures for speech enhancement. IEEE Trans. Audio Speech Lang. Process. 16(1), 229–238 (2008)
M.S. Islam, T.H. Al Mahmud, W.U. Khan, Z. Ye, Supervised single-channel speech enhancement based on stationary wavelet transforms and non-negative matrix factorization with concatenated framing process and subband smooth ratio mask. J. Sig. Process. Syst. Signal. Image Video Technol. 1–14 (2019)
M.S. Islam, T.H. Al Mahmud, W.U. Khan, Z. Ye, Supervised single-channel speech enhancement based on dual-tree complex wavelet transforms and nonnegative matrix factorization using the joint learning process and subband smooth ratio mask. Electronics 8, 353 (2019)
G.J. Jang, T.W. Lee, A maximum likelihood approach to single-channel source separation. J. Mach. Learn. Res. 4, 1365–1392 (2003)
D.S. Kapoor, A.K. Kohli, Gain adapted optimum mixture estimation scheme for single-channel speech separation. Circuits Syst. Signal Process. 32(5), 2335–2351 (2013)
J.M. Kates, K.H. Arehart, The hearing-aid speech perception index (HASPI). Speech Commun. 65, 75–93 (2014)
J.M. Kates, K.H. Arehart, The hearing-aid speech quality index (HASQI). J. Audio Eng. Soc. 58, 5363–5381 (2010)
N.G. Kingsbury, The dual-tree complex wavelet transforms: a new efficient tool for image restoration and enhancement, in Proceedings of the 9th European Signal Process Conference. EUSIPCO, Rhodes, Greece. 8–11 Sept (1998)
R.J. Le, F.J. Weninger, J.R. Hershey, Sparse NMF half-baked or well done? technical report TR2015–023, Mitsubishi Electric Research Laboratories (MERL), Cambridge, MA, USA, March (2015)
D. Lee, H.S. Seung, Algorithms for non-negative matrix factorization. Adv. Neural Inf. Process. Syst. 13, 556–562 (2001)
A. Mahmoodzadeh, H.R. Abutalebi, Hybrid approach to single-channel speech separation based on coherent incoherent modulation filtering. Circuits Syst. Signal Process. 36(5), 1970–1988 (2017)
S. Mavaddati, A novel singing voice separation method based on sparse non-negative matrix factorization and low-rank modeling. Iran. J. Electr. Electron. Eng. 15, 2 (2019)
P. Mercorelli, A denoising procedure using wavelet packets for instantaneous detection of pantograph oscillations. Mech. Syst. Signal Process. 35, 137–149 (2013)
P. Paatero, U. Tapper, Positive matrix factorization: a non-negative factor model with optimal utilization of error estimates of data values. Environmetrics 5(2), 111–126 (1994)
B.A. Pearlmutter, R.K. Olsson, Linear program differentiation for single-channel speech separation, in 16th IEEE Signal Processing Society Workshop in MLSP, Arlington, VA, USA (2006)
T. Pham, Y.S. Lee, Y.B. Lin, T.C. Tai, J.C. Wang, Single channel source separation using sparse nmf and graph regularization. ASE Big Data Soc. Inform. 55, 1–7 (2015)
B. Premanode, J. Vongprasert, C. Toumazou, Noise reduction for nonlinear nonstationary time series data using averaging intrinsic mode function. Algorithms 6(3), 407–429 (2013)
A.W. Rix, J.G. Beerends, M.P. Hollier, A.P. Hekstra, Perceptual evaluation of speech quality (PESQ)-a new method for speech quality assessment of telephone networks and codecs, in IEEE International Conference on Acoustics, Speech, Signal Processing. 6, 7–11 May (2001)
S.T. Roweis, One microphone source separation. Advances in Neural Information Processing Systems. 793–799 (2001).
S.T. Roweis, Factorial models and refiltering for speech separation and denoising, in Eurospeech, Geneva, 1009–1012 (2003)
M.N. Schmidt, R.K. Olsson, Single-channel speech separation using sparse non-negative matrix factorization, in 9th International Conference on Spoken Language Processing. Pittsburgh, PA, USA (2006)
M.N. Schmidt, M. Morup, Sparse non-negative matrix factor 2-D deconvolution for blind single-channel source separation. Indep. Compon. Anal. Blind Signal Sep. 3889, 700–707 (2006)
S.M. Seedahmed, A generalised wavelet packet‐based anonymization approach for ECG security application. 9, 18, 6137–6147 (2016)
L. Sun, C. Zhao, M. Su, F. Wang, Single-channel blind source separation based on joint dictionary with common sub-dictionary. Int. J. Speech Technol. 21(1), 19–27 (2018)
L. Sun, K. Xie, T. Gu, J. Chen, Z. Yang, Joint dictionary learning using a new optimization method for single-channel blind source separation. Speech Commun. 106, 85–94 (2019)
C.H. Tall, R.C. Hendriks, R. Heusdens, J. Jensen, An algorithm for intelligibility prediction of time-frequency weighted noisy speech. IEEE Trans. Audio Speech Lang. Process. 19(7), 2125–2136 (2011)
P. Tianliang, C. Yang, L. Zengli, A time-frequency domain blind source separation method for underdetermined instantaneous mixtures. Circuits Syst. Signal Process. 34(12), 3883–3895 (2015)
Y.V. Varshney, Z.A. Abbasi, M.R. Abidi, O. Farooq, Frequency selection based separation of speech signals with reduced computational time using sparse NMF. Arch. Acoust. 42(2), 287–295 (2017)
E. Vincent, R. Gribonval, C. Fevote, Performance measurement in blind audio source separation. IEEE Trans. Audio Speech Lang. Process. 14(4), 1462–1469 (2006)
S. Wang, A. Chern, Y. Tsao, J. Hung, X. Lu, Y. Lai, B. Su, Wavelet speech enhancement based on non-negative matrix factorization. IEEE Signal Process. Lett. 23, 1101–1105 (2016)
Y. Wang, Y. Li, K.C. Ho, A. Zare, M. Skubic, Sparsity promoted non-negative matrix factorization for source separation and detection, in Proceedings of the 19th International Conference on Digital Signal Processing. IEEE. 20–23 August (2014).
Z. Wanng, F. Sha, Discriminative non-negative matrix factorization for single-channel speech separation, in IEEE International Conference on Acoustics, Speech, and Signal Processing (2014)
Y. Xu, G. Bao, X. Xu, Z. Ye, Single-channel speech separation using sequential discriminative dictionary learning. Signal Process. 106, 134–140 (2015)
V.V. Yash, A.A. Zia, R.A. Musiur, O. Farooq, Variable sparsity regularization factor based SNMF for monaural speech separation, in 40th International Conference on Telecommunications and Signal Processing (TSP). 5–7 July (2017)
Acknowledgements
This research was supported by the National Natural Science Foundation of China (Grant No. 61671418).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Hossain, M.I., Islam, M.S., Khatun, M.T. et al. Dual-Transform Source Separation Using Sparse Nonnegative Matrix Factorization. Circuits Syst Signal Process 40, 1868–1891 (2021). https://doi.org/10.1007/s00034-020-01564-x
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00034-020-01564-x