On the Dissimilarity of Orthogonal Least Squares and Orthogonal Matching Pursuit Compressive Sensing Reconstruction

Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 27)

Abstract

Compressive sensing is a recent technique in the field of signal processing that aims to recover signals or images from half samples that were used by Shannon Nyquist theorem of reconstruction. For recovery using compressed sensing, two well known greedy algorithms are used- Orthogonal matching pursuit and orthogonal least squares. Generally these two algorithms are taken as same by the researchers which is not true. There is a remarkable difference between the two algorithms that is pointed out in this paper with the simulation results. The previous article clarifying the difference between these two algorithms are emphasized on theoretical difference and does not show any reconstruction simulation difference with these two algorithms and reason to preference over basis pursuit method . The key aim of this paper is to remove the confusion between the two algorithms on the basis of theory and reconstruction time taken with the output PSNR.

Keywords

Compressive sensing Reconstruction Orthogonal least squares orthogonal matching pursuit 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Donoho, D.L.: Compressed sensing. Stanford University Department of Statistics Technical Report (2004-2005)Google Scholar
  2. 2.
    Fornasier, M., Rauhut, H.: Compressive sensing. IEEE Transactions on Information Theory (2010)Google Scholar
  3. 3.
    Donoho, D.: Compressed sensing. IEEE Transactions on Information Theory 52(4), 1289–1306 (2006)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Blumensath, T., Davies, M.E.: On the difference between orthogonal matching pursuit and orthogonal least squares (2007)Google Scholar
  5. 5.
    Gillbert, T.: Signal recovery from random measurements via orthogonal matching pursuit. IEEE Transactions on Information Theory 53(12) (2007)Google Scholar
  6. 6.
    Beck, T.M.: Fast gradient based algorithms for constrained total variation image denoising and deblurring problems. IEEE Transactions on Image Processing 18, 2419–2434Google Scholar
  7. 7.
    Ehler, M., Fornasier, M., Sigl, J.: Quasi-Linear Compressed SensingGoogle Scholar
  8. 8.
    Soussen, C., Gribnovel, R.: Joint k-step analysis of orthogonal matching pursuit and orthogonal least squares. IEEE Transactions on Information Theory 59(5)Google Scholar
  9. 9.
    Vaswani, N.: LS-CS-Residual (LS-CS): Compressive Sensing on Least Squares Residual. IEEE Transactions on Signal Processing 58(8) (2010)Google Scholar
  10. 10.
    Vehkapera, M., Kabashima, Y., Chatterjee, S.: Analysis of Regularized LS Reconstruction and Random Matrix Ensembles in Compressed SensingGoogle Scholar
  11. 11.
    Candes, E., Romberg, J.: Sparsity and incoherence in compressive sampling. Inverse Problems 23(3), 969–985 (2007)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Gribonval, S., Herzet, I.: Sparse recovery conditions for orthogonal least squares. In: HAL 2 (2011)Google Scholar
  13. 13.
    Gharavi, H.T.S.: A fast orthogonal matching pursuit algorithm. In: IEEE International Conference on Acoustics, Speech and Signal Processing, vol. 3 (1998)Google Scholar
  14. 14.
    Kaur, A., Budhiraja, S.: In: Sparse signal reconstruction via orthogonal least squares. In: IEEE International Conference on ACCT (2014)Google Scholar
  15. 15.
    Rebollo-Neira, L., Lowe, D.: Optimized orthogonal matching pursuit approach. IEEE Signal Processing Letters 9(4) (2002)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Electronics and Communications EngineeringUIET, Panjab UniversityChandigarhIndia

Personalised recommendations