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Reseach Article

Speech Signal Reconstruction using Two-Step Iterative Shrinkage Thresholding Algorithm

by Rachit Saluja, Susmita Deb
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 153 - Number 11
Year of Publication: 2016
Authors: Rachit Saluja, Susmita Deb

Rachit Saluja, Susmita Deb . Speech Signal Reconstruction using Two-Step Iterative Shrinkage Thresholding Algorithm. International Journal of Computer Applications. 153, 11 ( Nov 2016), 1-4. DOI=10.5120/ijca2016912212

@article{ 10.5120/ijca2016912212,
author = { Rachit Saluja, Susmita Deb },
title = { Speech Signal Reconstruction using Two-Step Iterative Shrinkage Thresholding Algorithm },
journal = { International Journal of Computer Applications },
issue_date = { Nov 2016 },
volume = { 153 },
number = { 11 },
month = { Nov },
year = { 2016 },
issn = { 0975-8887 },
pages = { 1-4 },
numpages = {9},
url = { },
doi = { 10.5120/ijca2016912212 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
%0 Journal Article
%1 2024-02-06T23:58:49.553930+05:30
%A Rachit Saluja
%A Susmita Deb
%T Speech Signal Reconstruction using Two-Step Iterative Shrinkage Thresholding Algorithm
%J International Journal of Computer Applications
%@ 0975-8887
%V 153
%N 11
%P 1-4
%D 2016
%I Foundation of Computer Science (FCS), NY, USA

The idea behind Compressive Sensing(CS) is the reconstruction of sparse signals from very few samples, by means of solving a convex optimization problem. In this paper we propose a compressive sensing framework using the Two-Step Iterative Shrinkage/ Thresholding Algorithms(TwIST) for reconstructing speech signals. Further, we compare this framework with two other convex optimization algorithms, l1 Magic and Gradient Projection for Sparse Reconstruction(GPSR). The performance of our framework is demonstrated via simulations and exhibits a faster convergence rate and better peak signal-to-noise ratio(PSNR).

  1. Richard G Baraniuk. Compressive sensing. IEEE signal processing magazine, 24(4), 2007.
  2. Simon Foucart and Holger Rauhut. A mathematical introduction to compressive sensing, volume 1. Springer, 2013.
  3. Emmanuel Candes and Justin Romberg. Sparsity and incoherence in compressive sampling. Inverse problems, 23(3):969, 2007.
  4. Emmanuel J Cand`es, Justin Romberg, and Terence Tao. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Transactions on information theory, 52(2):489–509, 2006.
  5. Emmanuel J Cand`es and Michael B Wakin. An introduction to compressive sampling. Signal Processing Magazine, IEEE, 25(2):21–30, 2008.
  6. Thippur V Sreenivas and W Bastiaan Kleijn. Compressive sensing for sparsely excited speech signals. In 2009 IEEE International Conference on Acoustics, Speech and Signal Processing, pages 4125–4128. IEEE, 2009.
  7. Emmanuel J Candes and Terence Tao. Near-optimal signal recovery from random projections: Universal encoding strategies? IEEE transactions on information theory, 52(12):5406– 5425, 2006.
  8. Emmanuel J Cand`es et al. Compressive sampling. In Proceedings of the international congress of mathematicians, volume 3, pages 1433–1452. Madrid, Spain, 2006.
  9. Jos´e M Bioucas-Dias and M´ario AT Figueiredo. A new twist: two-step iterative shrinkage/thresholding algorithms for image restoration. IEEE Transactions on Image processing, 16(12):2992–3004, 2007.
  10. Emmanuel Candes and Justin Romberg. l1-magic: Recovery of sparse signals via convex programming. URL: www. acm. caltech. edu/l1magic/downloads/l1magic. pdf, 4:14, 2005.
  11. Robert D Nowak, Stephen J Wright, et al. Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems. IEEE Journal of selected topics in signal processing, 1(4):586–597, 2007.
  12. Wei Dai and Olgica Milenkovic. Subspace pursuit for compressive sensing signal reconstruction. IEEE Transactions on Information Theory, 55(5):2230–2249, 2009.
  13. Elaine T Hale,Wotao Yin, and Yin Zhang. A fixed-point continuation method for l1-regularized minimization with applications to compressed sensing. CAAM TR07-07, Rice University, 43:44, 2007.
  14. Thomas Blumensath and Mike E Davies. Iterative hard thresholding for compressed sensing. Applied and Computational Harmonic Analysis, 27(3):265–274, 2009.
  15. Emmanuel J Candes, Justin K Romberg, and Terence Tao. Stable signal recovery from incomplete and inaccurate measurements. Communications on pure and applied mathematics, 59(8):1207–1223, 2006.
Index Terms

Computer Science
Information Sciences


Compressive Sensing Convex Optimization Two-Step Iterative Shrinkage/Thresholding Algorithms l1 Magic Gradient Projection for Sparse Reconstruction