Skip to main content
SpringerLink
Log in

The Dantzig-Selector Algorithm

  • Chapter
  • First Online:
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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 49.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 99.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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.

    Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  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.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Science Department, The Technion – Israel Institute of Technology, 32000, Haifa, Israel

    Michael Elad

Authors
  1. Michael Elad
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michael Elad .

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

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

Download citation

Publish with us

Policies and ethics

Search

Navigation