Home   >   CSC-OpenAccess Library   >    Manuscript Information
Matrix Padding Method for Sparse Signal Reconstruction
Sabna N, P.R.Saseendran Pillai
Pages - 1 - 13     |    Revised - 31-1-2015     |    Published - 28-2-2015
Volume - 9   Issue - 1    |    Publication Date - January / February 2015  Table of Contents
Compressive Sensing, Greedy Algorithms, LMS Approximation, Relaxation Methods, Sparse Recovery, Sub-Nyquist Rate.
Compressive sensing has been evolved as a very useful technique for sparse reconstruction of signals that are sampled at sub-Nyquist rates. Compressive sensing helps to reconstruct the signals from few linear projections of the sparse signal. This paper presents a technique for the sparse signal reconstruction by padding the compression matrix for solving the underdetermined system of simultaneous linear equations, followed by an iterative least mean square approximation. The performance of this method has been compared with the widely used compressive sensing recovery algorithms such as l1_ls, l1-magic, YALL1, Orthogonal Matching Pursuit, Compressive Sampling Matching Pursuit, etc.. The sounds generated by 3-blade engine, music, speech, etc. have been used to validate and compare the performance of the proposed technique with the other existing compressive sensing algorithms in ideal and noisy environments. The proposed technique is found to have outperformed the l1_ls, l1-magic, YALL1, OMP, CoSaMP, etc. as elucidated in the results.
1 Google Scholar 
2 CiteSeerX 
3 refSeek 
4 Scribd 
5 SlideShare 
6 PdfSR 
D.L. Donoho. “Compressed Sensing.” IEEE Trans. Inform. Theory, vol. 52, no. 4, pp. 1289- 1305, Apr. 2006.
D.Needell and J.A.Tropp. “CoSaMP: Iterative Signal Recovery from Incomplete and Inaccurate Samples.” Applied Computational Harmonic Anal., vol. 26, no. 3, pp. 301–321, May 2009.
E. Candes, J. Romberg and T. Tao. “Stable Signal Recovery from Incomplete and Inaccurate Measurements.” Commun. Pure Applied Math., vol. 59, no. 8, pp. 1207-1223, Aug. 2006.
E. Cande`s and J. Romberg. “l1-MAGIC : Recovery of Sparse Signals via Convex Programming.” California Inst. Technol., Pasadena, CA, Tech. Rep., Oct. 2005. Available: http://users.ece.gatech.edu/~justin/l1magic/downloads/l1magic.pdf
E.J. Candes and M.B. Wakin. “An Introduction to Compressive Sampling.” IEEE Signal Process. Mag., pp. 21-30, Mar. 2008.
E.J. Candes and T. Tao. “Decoding by Linear Programming.” IEEE Trans. Inform. Theory, vol. 51, no. 12, pp. 4203-4215, Dec. 2005.
E.J. Candès. “Compressive sampling,” in Proc. Int. Congr. Mathematicians, Madrid, Spain, vol. 3, 2006, pp. 1433–1452.
J. Yang and Y. Zhang. “Alternating Direction Algorithms For l1-Problems In Compressive Sensing.” SIAM J. Scientific Computing, vol. 33, no. 1, pp. 250–278, 2011.
J.A. Tropp and A.C. Gilbert. “Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit.” IEEE Trans. Inform. Theory, vol. 53, no. 12, pp. 4655-4666, Dec. 2007.
J.A. Tropp and S.J. Wright. “Computational Methods for Sparse Solution of Linear Inverse Problems.” Proc. IEEE, vol. 98, no. 6, pp. 948-958, Jun. 2010.
J.A. Tropp. “Greed is Good: Algorithmic Results for Sparse Approximation.” IEEE Trans. Inform. Theory, vol. 50, no. 10, pp. 2231-2242, Oct. 2004.
K. Rao & P. Yip. Discrete Cosine Transform - Algorithms, Advantages, Applications. 1st Edition, Elsevier, Aug. 1990.
L. Vidya, V. Vivekananad, U. ShyamKumar, D. Mishra and R. Lakshminarayanan, “Feasibility Study of Applying Compressed Sensing Recovery Algorithms for Launch Vehicle Telemetry,” in IEEE Int. Conf. Microelectronics, Commun. Renewable Energy, 2013.
M.D. Plumbey, T. Blumensath, L. Daudet, R. Gribonval and M. Davis. “Sparse Representations in Audio and Music: From Coding to Source Separation.” Proc. IEEE, vol. 98, no. 6, pp. 995-1005, Jun. 2010.
Moreno-Alvarado and M. Martinez-Garcia. “DCT-Compressive Sampling of Frequency- sparse Audio Signals,” in Proc. World Congr. Eng. 2011, vol. II, London, UK, Jul. 2011.
R. Baraniuk, M. Davenport, R. DeVore and M. Wakin. “A simple proof of the Restricted Isometry Property for Random Matrices.” Constructive Approximation, vol. 28, no. 3, pp. 253–263, Dec. 2008.
R.G. Baraniuk, E. Candes, M. Elad and Y. Ma. “Applications of Sparse Representation and Compressive Sensing.” Proc. IEEE, vol. 98, no. 6, pp. 906-912, Jun. 2010.
R.G. Baraniuk, V. Cevher and M.B. Wakin. “Low-Dimensional Models for Dimensionality Reduction and Signal Recovery: A Geometric Perspective.” Proc. IEEE, vol. 98, no. 6, pp. 959-971, Jun. 2010.
R.G. Baraniuk. “Compressive sensing.” IEEE Signal Process. Mag., vol. 24, no. 4, pp. 118– 120,124, 2007.
S. Boyd and L. Vandenberghe. Convex Optimization, Cambridge University Press, 2004. Available: https://web.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf
S. Haykin. Adaptive Filter Theory. 3rd Edition, Prentice Hall, 1996.
S.J. Kim, K. Koh, M. Lustig, S. Boyd and D. Gorinevsky. “An Interior-Point method for Large-Scale l1-Regularized Least Squares.” IEEE J. Select. Topics Signal Process., vol. 1, no. 4, pp. 606–617, Dec. 2007.
Y. Chen, Y. Gu and A.O. Hero III. “Sparse LMS for system identification,” in IEEE Int. Conf. Acoustics, Speech and Signal Process, Apr. 2009, pp. 3125 – 3128.
Y. Gu, J. Jin and S. Mei. “lo Norm Constraint LMS Algorithm For Sparse System Identification.” IEEE Signal Process. Letters, vol. 16, no. 9, pp. 774-777, Sept. 2009.
Y. Zhang, J. Yang and W. Yin. “User’s guide for YALL1: Your algorithms for L1 Optimization.” Tech. Rep., 2010. [Online]. Available: http://www.caam.rice.edu/~optimization/L1/YALL1/User_Guide/YALL1v1.0_User_Guide.pdf
Miss Sabna N
Department of Electronics, Cochin University of Science and Technology, Cochin 682 022, India - India
Professor P.R.Saseendran Pillai
Department of Electronics - India