Abstract
Speech enhancement using Compressive Sensing algorithm is a different paradigm from the conventional enhancement and compression techniques. Compressive Sensing requires very less number of samples compared to the Nyquist sampling for the purpose of reconstructing the signal. This work provides a comparative analysis of three sparsifying basis functions DFT, DCT and DWT for compressive speech enhancement on the basis of five objective measures. The objective measures used are: Signal to Noise Ratio, Segmental Signal to Noise Ratio, Log-Likelihood Ratio, Perceptual Evaluation of Speech Quality and processing time. Experimental analysis concludes that DWT as a basis function performs better than the others for compressive speech enhancement. As orthogonal wavelets are suitable for signal denoising, this work further investigates the performance of the four orthogonal wavelet families: Daubechies, Coiflets, Symlets and Fejér-Korovkin as basis functions for the purpose of compressive speech enhancement.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abo-Zahhad, M., Hussein, A., & Mohamed, A. (2015). Compressive sensing algorithms for signal processing applications: A survey. International Journal of Communications, Network and System Sciences, 8, 197–216. https://doi.org/10.4236/ijcns.2015.86021.
Abrol,V., Sharma, P., & Budhiraja, S. (2013). Evaluating performance of compressed sensing for speech signals. In: IEEE 3rd international advance computing conference (IACC) (pp. 1159–1164).
Baraniuk, R. (2007). Compressive sensing. IEEE Signal Processing Magazine, 24, 118–121.
Baraniuk, R. G., Davenport, M., DeVore, R., & Wakin, M. (2008). A simple proof of the restricted isometry property for random matrices. Constructive Approximation, 28, 253–263. https://doi.org/10.1007/s00365-007-9003-x.
Candès, E. J. (2008). The restricted isometry property and its implications for compressed sensing. Comptes Rendus Mathematique Academie des Sciences Series I, 346(9–10), 589–592. https://doi.org/10.1016/j.crma.2008.03.014.
Candès, E., & Romberg, J. (2005). L1-magic: Recovery of sparse signals via convex programming. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.212.9120. Retrieved Oct 14, 2015.
Candès, E. J., & Romberg, J. (2007). Sparsity and incoherence in compressive sampling. Inverse Problems, 23(3), 969–985. https://doi.org/10.1088/0266-5611/23/3/008.
Candès, E. J., Romberg, J., & Tao, T. (2006). Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Transactions on Information Theory, 52, 489–509. https://doi.org/10.1109/TIT.2005.862083.
Candès, E. J., & Wakin, M. B. (2008). An introduction to compressive sampling. IEEE Signal Processing Magazine, 25(2), 21–30. https://doi.org/10.1109/MSP.2007.914731.
Christensen, M. G., Ostergaard, J., & Jensen, S. H. (2009). On compressed sensing and its application to speech and audio signals. In: Asilomar conference on signals, systems and computers (pp. 356–360). https://doi.org/10.1109/ACSSC.2009.5469828.
Compressive sensing resources, Digital signal processing at Rice University. http://dsp.rice.edu/cs/. Retrieved Nov 8, 2018.
Davenport, M. A., Boufounos, P. T., Wakin, M. B., & Baraniuk, R. G. (2010). Signal processing with compressive measurements. IEEE Journal of Selected Topics in Signal Processing, 4(2), 445–460. https://doi.org/10.1109/JSTSP.2009.2039178.
Davenport, M., Duarte, M., Eldar, Y., & Kutyniok, G. (2011). Introduction to compressed sensing. In Y. C. Eldar & G. Kutyniok (Eds.), Compressed sensing: Theory and applications (pp. 1–68). Cambridge: Cambridge University Press.
Donoho, D. L. (2004). For most underdetermined systems of linear equations, the minimal l 1 solution is also the sparsest solution. Communications on Pure and Applied Mathematics, 59, 797–829. https://doi.org/10.1002/cpa.20132.
Donoho, D. L. (2006). Compressed sensing. IEEE Transactions on Information Theory, 52(4), 1289–1306. https://doi.org/10.1109/TIT.2006.871582.
Donoho, D., Elad, M., & Temlyakov, V. (2006). Stable recovery of sparse overcomplete representations in the presence of noise. IEEE Transactions on Information Theory, 52(1), 6–18. https://doi.org/10.1109/TIT.2005.860430.
Firouzeh, F. F., Ghorshi, S., & Salsabili, S. (2014). Compressed sensing based speech enhancement. In: 8th international conference on signal processing and communication systems (ICSPCS) (pp. 1–6). https://doi.org/10.1109/ICSPCS.2014.7021068.
Foucart, S., & Rauhut, H. (2013). A mathematical introduction to compressive sensing. Basel: Birkhäuser.
Gao, Y., Liu, G., Wang, G., Min, G.,& Du, J. (2011). Research on speech characteristics based on compressed sensing theory. In: Second international conference on mechanic automation and control engineering (MACE) (pp. 637–640). https://doi.org/10.1109/MACE.2011.5987005.
Giacobello, D., Christensen, M. G., Murthi, M. N., Jensen, S. H., & Moonen, M. (2009). Retrieving sparse patterns using a compressed sensing framework: Applications to speech coding based on sparse linear prediction. IEEE Signal Processing Letters, 17(1), 103–106. https://doi.org/10.1109/LSP.2009.2034560.
Graps, A. (1995). An introduction to wavelets. IEEE Computational Science and Engineering, 2(2), 50–61. https://doi.org/10.1109/99.388960.
Hermann, V. (2016). Wavelets II: Vanishing moments and spectral factorization. https://www.dsprelated.com/showarticle/1006.php. Retrieved Feb 2, 2018.
Holtz, O.V. (2008). Compressive sensing: A paradigm shift in signal processing. CoRR, abs/0812.3137. https://arxiv.org/abs/0812.3137. Retrieved Oct 1, 2015.
Hu, Y., & Loizou, P. C. (2008). Evaluation of objective quality measures for speech enhancement. IEEE Transactions on Audio, Speech and Language Processing, 16(1), 229–238. https://doi.org/10.1109/TASL.2007.911054.
ITU. (2001). Perceptual evaluation of quality (PESQ): An objective method for end-to-end speech quality assessment of narrow-band telephone networks and speech codecs. ITU-T Recommendation (p. 862).
Kutyniok, G. (2013). Theory and applications of compressed sensing. GAMM-Mitteilungen. https://arxiv.org/abs/1203.3815. Retrieved Sep 29, 2015.
l 1-Magic. https://statweb.stanford.edu/~candes/l1magic/. Retrieved July 27, 2018.
Loizou, P. C. (2013). Speech enhancement: Theory and practice (2nd ed.). Boca Raton: CRC Press.
Low, S. Y., Pham, D. S., & Venkatesh, S. (2013). Compressive speech enhancement. Speech Communication, 55(6), 757–768. https://doi.org/10.1016/j.specom.2013.03.003.
Mallat, S. (2009). A wavelet tour of signal processing: The sparse way (3rd ed.). London: Academic Press.
MathWorks, Wavelet Toolbox.https://in.mathworks.com/help/wavelet/gs/choose-a-wavelet.html. Retrieved Jan 11, 2018.
Misiti, M., Misiti, Y., Oppenheim, G., & Poggi J.-M. (2009). Wavelet Toolbox™ 4 user’s guide, The MathWorks.
Needell, D., & Tropp, J. A. (2009). CoSaMP: Iterative signal recovery from incomplete and inaccurate samples. Applied and Computational Harmonic Analysis, 26(3), 301–321. https://doi.org/10.1016/j.acha.2008.07.002.
Nielsen, M. (2001). On the construction and frequency localization of finite orthogonal quadrature filters. Journal of Approximation Theory, 108(1), 36–52. https://doi.org/10.1006/jath.2000.3514.
NOIZEUS: A noisy speech corpus for evaluation of speech enhancement algorithms. http://ecs.utdallas.edu/loizou/speech/noizeus/. Retrieved Sep 21, 2015.
Parkale, Y. V., & Nalbalwar, S. L. (2018). Application of 1-D discrete wavelet transform based compressed sensing matrices for speech compression. Springer Plus, 5(2048), 1–60.
Pilastri, A. L., Manuel, J., & Tavares, R. S. (2016). Reconstruction algorithms in compressive sensing: An overview. In: Proceedings of the doctoral symposium in informatics and telecommunications engineering (DSIE’16) (pp. 127–137), Portugal.
Savic, T., & Albijanic, R. (2015). CS reconstruction of the speech and musical signals. In: 4th Mediterranean conference on embedded computing (MECO) (pp. 299–302). https://doi.org/10.1109/MECO.2015.7181927.
Selesnick, I. (2012). Introduction to sparsity in signal processing. A tutorial on sparsity-based methods in signal processing, OpenStax-CNX module: m43545, version 1.3. http://eeweb.poly.edu/iselesni/teaching/lecture_notes/sparsity_intro/. Retrieved Dec 17, 2016.
Sreenivas, T. V. & Kleijn, W. B. (2009). Compressive sensing for sparsely excited speech signals. In: Proceedings of IEEE international conference of acoustics, speech and signal processing (pp. 4125–4128). https://doi.org/10.1109/ICASSP.2009.4960536.
Strohmer, T. (2012). Measure what should be measured: progress and challenges in compressive sensing. IEEE Signal Processing Letters, 19(12), 887–893. https://arxiv.org/abs/1210.6730. Retrieved Sep 29, 2015.
Unser, M. (1996). Vanishing moments and the approximation power of wavelet expansions. In: Proceedings of the 3rd IEEE international conference on image processing (ICIP’96) (vol. I, pp. 629–632), Lausanne, Switzerland. https://doi.org/10.1109/ICIP.1996.559575.
Waters, A., & Cevher, V. (2008). The CoSamp algorithm. Lecture Notes by Rice University, STAT 631/ELEC 639.
Wu, D., Zhu, W. P., & Swamy, M. N. S. (2012). On sparsity issues in compressive sensing based speech enhancement. In: IEEE international symposium on circuits and systems (ISCAS) (pp. 285–288). https://doi.org/10.1109/ISCAS.2012.6271907.
Xu, S. F., & Chen, X. B. (2015). Speech signal acquisition methods based on compressive sensing. Systems and computer technology (pp. 115–120). London: Taylor and Francis Group.
Yang H., Hao, D., Sun, H., & Liu, Y. (2014). Speech enhancement using orthogonal matching pursuit algorithm. IEEE international conference on in orange technologies (ICOT) (pp. 101–104). https://doi.org/10.1109/ICOT.2014.6956609.
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
Sahu, S., Rayavarapu, N. Performance comparison of sparsifying basis functions for compressive speech enhancement. Int J Speech Technol 22, 769–783 (2019). https://doi.org/10.1007/s10772-019-09622-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10772-019-09622-9