Reconstruction Using Sparse Approximation

  • Rana Sameer Pratap Singh
  • Rosepreet Kaur Bhogal
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 624)


Interest in sparse approximations is prevalent in the recent years. The reason for this undivided engrossment is due to the large amount of applications. The process to find a sparse approximation can be very cumbersome since there is no specific method that can guarantee a solution in every situation. In this paper, we find sparse approximations and then analyze two algorithms: orthogonal matching pursuit (OMP) and least square orthogonal matching pursuit (LS-OMP).


Algorithms Approximation methods Least square Orthogonal matching pursuit (OMP) Sparse 


  1. 1.
    R. A. DeVore, “Nonlinear approximation,” Acta Num., pp. 51–150, (1998).Google Scholar
  2. 2.
    V. Temlyakov, “Nonlinear methods of approximation,” Foundations of Comp. Math., vol. 3, no. 1, pp. 33–107, July (2003).Google Scholar
  3. 3.
    G. Davis, S. Mallat, and M. Avellaneda, “Greedy adaptive approximation,” J. Constr. Approx., vol. 13, pp. 57–98, (1997).Google Scholar
  4. 4.
    A. C. Gilbert, M. Muthukrishnan, and M. J. Strauss, “Approximation of functions over redundant dictionaries using coherence,” in Proc. 14th Annu. ACM-SIAM Symp. Discrete Algorithms, Baltimore, MD, pp. 243–252, Jan. (2003).Google Scholar
  5. 5.
    Charles Soussen, Remi Gribonval, Jerome Idier, and Cedric Herzet, “Joint k-step analysis of orthogonal matching pursuit and orthogonal least squares,” IEEE Trans. Inform. Theory, vol. 59, no. 5, pp. 3158–3174, May (2013).Google Scholar
  6. 6.
    Gagan rath and Christine guillemot, “Sparse approximation with an orthogonal complementary matching pursuit algorithm,” IEEE trans., pp. 3325–3328, (2009).Google Scholar
  7. 7.
    Joel A. Tropp, “Greed is Good: Algorithmic results for sparse approximation,” IEEE Trans Inform. Theory, vol. 50, no. 10, pp. 2231–2242, Oct (2004).Google Scholar
  8. 8.
    Emmanuel J. Candes and Terence Tao, “Near-Optimal signal recovery from random projections: universal encoding strategies,” IEEE Trans. Inform. Theory, vol. 52, no. 12, pp. 5406–5425, Dec (2006).Google Scholar
  9. 9.
    Michael Elad and Alfred M. Bruckstein, “A generalized uncertainty principle and sparse representation in pairs of bases,” IEEE Trans. Inform. Theory, vol. 48, no. 9, pp. 2558–2567, Sept (2002).Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Rana Sameer Pratap Singh
    • 1
  • Rosepreet Kaur Bhogal
    • 1
  1. 1.Lovely Professional UniversityPhagwaraIndia

Personalised recommendations