Abstract
M-FOCUSS is one of the most successful and efficient methods for sparse representation. To reduce the computational cost of M-FOCUSS and to extend its availability for large scale problems, M-FOCUSS is extended to CG-M-FOCUSS by incorporating conjugate gradient (CG) iterations in this paper. Furthermore, the CG-M-FOCUSS is applied to distributed compressed sensing. We illustrate the performance of CG-M-FOCUSS by an MRI image reconstruction example, in which CG-M- FOCUSS can not only reconstruct the MRI image with high precision, but also considerably reduce the computational time.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Kim, S.J., Koh, K., Lustig, M., Boyd, S., Gorinevsky, D.: An interior-point method for large-scale ℓ1-regularized least squares. IEEE Journal on Selected Topics in Signal Processing 4(1), 606–617 (2007)
Rao, B.D.: Signal processing with the sparseness constraint. In: Proceedings of the ICASSP, Seattle, WA, vol. III, pp. 1861–1864 (1998)
Cichocki, A., Amari, S.: Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications. John Wiley & Sons, New York (2003)
Mallat, S.G., Zhang, Z.: Matching pursuits with time-frequency dictionaries. IEEE Trans. Signal Processing 41(12), 3397–3415 (1993)
Tropp, J.: Greed is good: algorithmic results for sparse approximation. IEEE Trans. Information Theory 50(10), 2231–2242 (2004)
Chen, S., Donoho, D.L., Saunders, M.A.: Atomic decomposition by basis pursuit. SIAM Journal on Scientific Computing 20(1), 33–61 (1998)
Donoho, D.L., Elad, M.: Maximal sparsity representation via ℓ1 minimization. In: Proc. National Academy Science, vol. 100, pp. 2197–2202 (2003)
Li, Y.Q., Cichocki, A., Amari, S.: Analysis of sparse representation and blind source separation. Neural Computation 16, 1193–1234 (2004)
Takigawa, I., Kudo, M., Toyama, J.: Performance analysis of minimum ℓ1-norm solutions for underdetermined source separation. IEEE Trans. Signal Processing 52(3), 582–591 (2004)
Li, Y.Q., Amari, S., Cichocki, A., Ho, D.W.C., Xie, S.L.: Underdetermined blind source separation based on sparse representation. IEEE Trans. Signal Processing 54(2), 423–437 (2006)
Bofill, P., Zibulevsky, M.: Underdetermined blind source separation using sparse representations. Signal Processing 81, 2353–2362 (2001)
Gorodnitsky, I.F., George, J., Rao, B.D.: Neuromagnetic source imaging with FOCUSS: A recursive weighted minimum norm algorithm. Electroencephalography and Clinical Neurophysiology 95(4), 231–251 (1995)
Rao, B.D., Kreutz-Delgado, K.: Deriving algorithms for computing sparse solutions to linear inverse problems. In: Conference Record of the Thirty-First Asilomar Conference on Signals, Systems and Computers, vol. 1, pp. 955–959 (1997)
Gorodnitsky, I.F., Rao, B.D.: Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm. IEEE Trans. Signal Processing 45(3), 600–616 (1997)
Rao, B.D., Kreutz-Delgado, K.: An affine scaling methodology for best basis selection. IEEE Trans. Signal Processing 47(1), 187–200 (1999)
Kreutz-Delgado, K., Murry, J.F., Rao, B.D., et al.: Dictionary learning algorithms for sparse representation. Neural Computation 15, 349–396 (2003)
Cotter, S.F., Rao, B.D., Engan, K., Kreutz-Delgado, K.: Sparse solutions to linear inverse problems with multiple measurement vectors. IEEE Trans. Signal Processing 53(7), 2477–2488 (2005)
Baraniuk, R.: Compressive sensing. IEEE Signal Processing Magazine 24(4), 118–121 (2007)
Donoho, D.: Compressed sensing. IEEE Trans. on Information Theory 52(4), 1289–1306 (2006)
Duarte, M., Davenport, M., Takhar, D., Laska, J., Sun, T., Kelly, K., Baraniuk, R.: Single-pixel imaging via compressive sampling. IEEE Signal Processing Magazine 25(2), 83–91 (2008)
Hestenes, M.R., Stiefel, E.: Methods of conjugate gradients for solving linear systems. Journal of Research of the National Bureau of Standards 49(6), 409–436 (1952)
Nocedal, J., Wright, S.J.: Numerical optimization, 2nd edn. Springer series in operations research and financial engineering. Springer, New York (2006)
Duarte, M., Sarvotham, S., Baron, D., Wakin, M., Baraniuk, R.: Distributed compressed sensing of jointly sparse signals. In: Conference Record of the Thirty-Ninth Asilomar Conference on Signals, Systems and Computers, pp. 1537–1541 (2005)
Lustig, M., Donoho, D.L., Santos, J.M., Pauly, J.M.: Compressed sensing MRI. IEEE Signal Processing Magazine 25(2), 72–82 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
He, Z., Cichocki, A., Zdunek, R., Cao, J. (2008). CG-M-FOCUSS and Its Application to Distributed Compressed Sensing. In: Sun, F., Zhang, J., Tan, Y., Cao, J., Yu, W. (eds) Advances in Neural Networks - ISNN 2008. ISNN 2008. Lecture Notes in Computer Science, vol 5263. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87732-5_27
Download citation
DOI: https://doi.org/10.1007/978-3-540-87732-5_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87731-8
Online ISBN: 978-3-540-87732-5
eBook Packages: Computer ScienceComputer Science (R0)