Abstract
Signal sampling is an important concern for compressive sensing framework. The use of efficient sampling may enhance the overall performance by collecting informative samples. The work done in this paper is aimed to propose the efficient sampling matrix for speech compressive sensing by reviewing the reconstruction results obtained via conventionally used measurement matrices. Recently used measurement matrices are either randomly structured or deterministic in nature. Therefore, the prime objective of this work is to analyse speed and reconstruction performance of ℓ1-norm minimization algorithm when samples are provided by the concerned sampling matrix. The speed and accuracy analysis is intended to propose efficient sampling matrix which can facilitate faithful signal reconstruction process for speech compressive sensing. The sampling matrices chosen for this work are Bernoulli random matrix, Gaussian random matrix, Hadamard matrix and Toeplitz matrix. The observed matrices are carefully adjusted to provide different range of sampling ratios for signal recovery process. In this work, the number of input samples are changed (from 10% to 40%) to search for the efficient sampling matrix which can survive the least possible number of samples. The performances of the sampling matrices are compared on the basis of Root Mean Squared Error (RMSE) values and reconstruction time (in seconds) is obtained via ℓ1 minimization method.
Similar content being viewed by others
References
Ahmed I, Ahmad N, Ali H, Ahmad G (2012) The development of isolated words pashto automatic speech recognition system. In: 2012 18th international conference on automation and computing (ICAC). IEEE, pp 1–4
Ahmed I, Ali H, Ahmad N, Ahmad G (2012) The development of isolated words corpus of pashto for the automatic speech recognition research. In: 2012 international conference of robotics and artificial intelligence. IEEE, pp 139–143
Ahmed I, Khan A, Ahmad N, Ali H, et al. (2020) Speech signal recovery using block sparse bayesian learning. Arab J Sci Eng 45(3):1567–1579
Arjoune Y, Kaabouch N, Ghazi HE, Tamtaoui A (2017) Compressive sensing: performance comparison of sparse recovery algorithms. In: 2017 IEEE 7th annual computing and communication workshop and conference (CCWC). IEEE, pp 1–7
Arjoune Y, Kaabouch N, Ghazi HE, Tamtaoui A (2018) A performance comparison of measurement matrices in compressive sensing. Int J Commun Syst 31(10):e3576
Bala S, Arif M (2015) Effect of sparsity on speech compressed sensing. In: 2015 international conference on signal processing, computing and control (ISPCC). IEEE, pp 81–86
Candès EJ, Wakin MB (2008) An introduction to compressive sampling. IEEE Signal Processing Magazine 25(2):21–30
Carrillo RE, Ramirez AB, Arce GR, Barner KE, Sadler BM (2016) Robust compressive sensing of sparse signals: a review. EURASIP Journal on Advances in Signal Processing 2016(1):108
Chen SS, Donoho DL, Saunders MA (2001) Atomic decomposition by basis pursuit. SIAM Rev 43(1):129–159
Deng C, Lin W, Lee B-s, Lau CT (2010) Robust image compression based on compressive sensing. In: 2010 IEEE international conference on multimedia and expo (ICME). IEEE, p 2010
Dias U, Rane ME (2013) Comparative analysis of sensing matrices for compressed sensed thermal images. In: 2013 international mutli-conference on automation, computing, communication, control and compressed sensing (imac4s). IEEE, pp 265–270
Donoho DL (2006) Compressed sensing. IEEE Transactions on Information Theory 52(4):1289–1306
Haider H, Shah JA, Ali U (2014) Comparative analysis of sparse signal recovery algorithms based on minimization norms. In: World congress on sustainable technologies (WCST-2014). IEEE, pp 72–76
Nguyen TLN, Shin Y (2013) Deterministic sensing matrices in compressive sensing: a survey. Sci World J 2013(4). https://doi.org/10.1155/2013/192795
Pearlsy PV, Sankar D (2018) Implementation of compressive sensing for speech signals. In: 2018 8th international symposium on embedded computing and system design (ISED). IEEE, pp 162–166
Qaisar S, Bilal RM, Iqbal W, Naureen M, Lee S (2013) Compressive sensing: from theory to applications, a survey. Journal of Communications and networks 15(5):443–456
Salan S, Muralidharan KB (2017) Image reconstruction based on compressive sensing using optimized sensing matrix. In: 2017 international conference on intelligent computing, instrumentation and control technologies (ICICICT). IEEE, pp 252–256
Tang X, Wu S, Dong R, Xia G (2018) Application of compressed sensing theory in the sampling and reconstruction of speech signals. In: 2nd international forum on management, education and information technology application (IFMEITA 2017). Atlantis Press
Wang Z, Bovik AC (2009) Mean squared error: love it or leave it? A new look at signal fidelity measures. IEEE Signal Processing Magazine 26(1):98–117
Wei Z, Zhang J, Xu Z, Liu Y (2020) Measurement matrix optimization via mutual coherence minimization for compressively sensed signals reconstruction. Math Probl Eng, 2020. https://doi.org/10.1155/2020/7979606
Yin M, Yu K, Wang Z (2016) Compressive sensing based sampling and reconstruction for wireless sensor array network. Math Probl Eng, 2016
Zaeemzadeh A, Joneidi M, Rahnavard N (2017) Adaptive non-uniform compressive sampling for time-varying signals. arXiv:1703.03340
Zhang Z, Wei S, Wei D, Lin L, Liu F, Liu C (2016) Comparison of four recovery algorithms used in compressed sensing for ecg signal processing. In: Proceedings of the Computing in Cardiology Conference (CinC), Vancouver, BC, Canada, pp 11–14
Funding
This research received no external funding.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of Interests
The authors declare no conflict of interest.
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
Ahmed, I., Khan, A., Khan, A. et al. Efficient measurement matrix for speech compressive sampling. Multimed Tools Appl 80, 20327–20343 (2021). https://doi.org/10.1007/s11042-021-10657-x
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11042-021-10657-x