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The Dantzig-Selector Algorithm

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Sparse and Redundant Representations

Abstract

In this chapter we present an appealing and surprising alternative pursuit algorithm for sparse approximation. This algorithm is competitive with the Basis Pursuit Denoising (BPDN) and the OMP. This algorithm was proposed in 2007 by Candes and Tao, and termed Dantzig-Selector (DS). The name chosen pays tribute to George Dantzig, the father of the simplex algorithm that solves Linear Programming (LP) problems. The connection to LP will become evident shortly.

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Further Reading

  1. Z. Ben-Haim, Y.C. Eldar, and M. Elad, Coherence-based performance guarantees for estimating a sparse vector under random noise, submitted to IEEE Transactions on Signal Processing, 2009.

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  2. P.J. Bickel, Y. Ritov, and A. Tsybakov, Simultaneous analysis of Lasso and Dantzig selector, to appear in Ann. Statist., 2008.

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  3. E.J. Candès and T. Tao, Decoding by linear programming, IEEE Trans. on Information Theory, 51(12):4203–4215, December 2005.

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  4. E.J. Candès and T. Tao, The Dantzig selector: Statistical estimation when p is much larger than n, Annals of Statistics, 35(6):2313–2351, June 2007.

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  5. G.M. James, P. Radchenko, and J. Lv, DASSO: connections between the Dantzig selector and lasso, Journal of the Royal Statist. Soc. B, 71(1):127–142, 2009.

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  6. N. Meinshausen, G. Rocha, and B. Yu, Discussion: A tale of three cousins: Lasso, L2Boosting and Dantzig, Ann. Statist., 35(6):2373–2384, 2007.

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  7. J.L. Starck, D.L. Donoho and E. Candès, Very high quality image restoration, in SPIE conference on Signal and Image Processing: Wavelet Applications in Signal and Image Processing IX, Vol 4478, 2001.

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Correspondence to Michael Elad .

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Elad, M. (2010). The Dantzig-Selector Algorithm. In: Sparse and Redundant Representations. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7011-4_8

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