Performance comparison of sparsifying basis functions for compressive speech enhancement

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.

[1]  E.J. Candes,et al.  An Introduction To Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[2]  Svetha Venkatesh,et al.  Compressive speech enhancement , 2013, Speech Commun..

[3]  Sanjay L. Nalbalwar,et al.  Application of 1-D discrete wavelet transform based compressed sensing matrices for speech compression , 2016, SpringerPlus.

[4]  R. DeVore,et al.  A Simple Proof of the Restricted Isometry Property for Random Matrices , 2008 .

[5]  Thomas Strohmer,et al.  Measure What Should be Measured: Progress and Challenges in Compressive Sensing , 2012, ArXiv.

[6]  Aswin C. Sankaranarayanan,et al.  Compressive Sensing , 2008, Computer Vision, A Reference Guide.

[7]  R.G. Baraniuk,et al.  Compressive Sensing [Lecture Notes] , 2007, IEEE Signal Processing Magazine.

[8]  E. Candès.  The restricted isometry property and its implications for compressed sensing , 2008 .

[9]  D. Donoho.  For most large underdetermined systems of linear equations the minimal 𝓁1‐norm solution is also the sparsest solution , 2006 .

[10]  Stéphane Mallat,et al.  A Wavelet Tour of Signal Processing - The Sparse Way, 3rd Edition , 2008 .

[11]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[12]  J. Tropp,et al.  CoSaMP: Iterative signal recovery from incomplete and inaccurate samples , 2008, Commun. ACM.

[13]  Shu-Fang Xu,et al.  Speech signal acquisition methods based on compressive sensing , 2015 .

[14]  Yi Hu,et al.  Evaluation of Objective Quality Measures for Speech Enhancement , 2008, IEEE Transactions on Audio, Speech, and Language Processing.

[15]  Amara Lynn Graps,et al.  An introduction to wavelets , 1995 .

[16]  Morten Nielsen,et al.  On the Construction and Frequency Localization of Finite Orthogonal Quadrature Filters , 2001, J. Approx. Theory.

[17]  Richard G. Baraniuk,et al.  Signal Processing With Compressive Measurements , 2010, IEEE Journal of Selected Topics in Signal Processing.

[18]  Holger Rauhut,et al.  A Mathematical Introduction to Compressive Sensing , 2013, Applied and Numerical Harmonic Analysis.

[19]  Aziza I. Hussein,et al.  Compressive Sensing Algorithms for Signal Processing Applications: A Survey , 2015 .

[20]  Seyed Ghorshi,et al.  Compressed sensing based speech enhancement , 2014, 2014 8th International Conference on Signal Processing and Communication Systems (ICSPCS).

[21]  Mads Graesbll Christensen,et al.  On compressed sensing and its application to speech and audio signals , 2009, 2009 Conference Record of the Forty-Third Asilomar Conference on Signals, Systems and Computers.

[22]  P. Sharma,et al.  Evaluating performance of Compressed Sensing for speech signals , 2013, 2013 3rd IEEE International Advance Computing Conference (IACC).

[23]  B. Sarkar,et al.  Interval-valued fuzzy $$\phi$$ϕ-tolerance competition graphs , 2016, SpringerPlus.

[24]  Yue Gao,et al.  Research on speech characteristics based on compressed sensing theory , 2011, 2011 Second International Conference on Mechanic Automation and Control Engineering.

[25]  Yonina C. Eldar,et al.  Introduction to Compressed Sensing , 2022 .

[26]  Michael Elad,et al.  Stable recovery of sparse overcomplete representations in the presence of noise , 2006, IEEE Transactions on Information Theory.

[27]  Marc Moonen,et al.  Retrieving Sparse Patterns Using a Compressed Sensing Framework: Applications to Speech Coding Based on Sparse Linear Prediction , 2010, IEEE Signal Processing Letters.

[28]  Thippur V. Sreenivas,et al.  Compressive sensing for sparsely excited speech signals , 2009, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing.

[29]  Trifun Savic,et al.  CS reconstruction of the speech and musical signals , 2015, 2015 4th Mediterranean Conference on Embedded Computing (MECO).

[30]  Philipos C. Loizou,et al.  Speech Enhancement: Theory and Practice , 2007 .

[31]  Hongwu Yang,et al.  Speech enhancement using orthogonal matching pursuit algorithm , 2014, 2014 International Conference on Orange Technologies.

[32]  Michael Unser,et al.  Vanishing moments and the approximation power of wavelet expansions , 1996, Proceedings of 3rd IEEE International Conference on Image Processing.

[33]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[34]  E. Candès,et al.  Sparsity and incoherence in compressive sampling , 2006, math/0611957.

[35]  Wei-Ping Zhu,et al.  On sparsity issues in compressive sensing based speech enhancement , 2012, 2012 IEEE International Symposium on Circuits and Systems.