OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 30, Iss. 4 — Apr. 1, 2013
  • pp: 758–768

Sparse representation of astronomical images

Laura Rebollo-Neira and James Bowley  »View Author Affiliations


JOSA A, Vol. 30, Issue 4, pp. 758-768 (2013)
http://dx.doi.org/10.1364/JOSAA.30.000758


View Full Text Article

Enhanced HTML    Acrobat PDF (449 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Sparse representation of astronomical images is discussed. It is shown that a significant gain in sparsity is achieved when particular mixed dictionaries are used for approximating these types of images with greedy selection strategies. Experiments are conducted to confirm (i) the effectiveness at producing sparse representations and (ii) competitiveness, with respect to the time required to process large images. The latter is a consequence of the suitability of the proposed dictionaries for approximating images in partitions of small blocks. This feature makes it possible to apply the effective greedy selection technique called orthogonal matching pursuit, up to some block size. For blocks exceeding that size, a refinement of the original matching pursuit approach is considered. The resulting method is termed “self-projected matching pursuit,” because it is shown to be effective for implementing, via matching pursuit itself, the optional backprojection intermediate steps in that approach.

© 2013 Optical Society of America

OCIS Codes
(100.2000) Image processing : Digital image processing
(100.2960) Image processing : Image analysis

ToC Category:
Image Processing

History
Original Manuscript: September 10, 2012
Revised Manuscript: December 20, 2012
Manuscript Accepted: December 28, 2012
Published: March 27, 2013

Citation
Laura Rebollo-Neira and James Bowley, "Sparse representation of astronomical images," J. Opt. Soc. Am. A 30, 758-768 (2013)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-4-758


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. S. Fischer, G. Cristóbal, and R. Redondo, “Sparse overcomplete Gabor wavelet representation based on local competitions,” IEEE Trans. Image Process. 15, 265–272 (2006). [CrossRef]
  2. J. Mairal, M. Eldar, and G. Sapiro, “Sparse representation for color image restoration,” IEEE Trans. Image Process. 17, 53–69 (2008). [CrossRef]
  3. L. P. Yaroslavsky, G. Shabat, B. G. Salomon, I. A. Ideses, and B. Fishbain, “Nonuniform sampling, image recovery from sparse data and the discrete sampling theorem,” J. Opt. Soc. Am. A 26, 566–575 (2009). [CrossRef]
  4. J. Wright, Yi Ma, J. Mairal, G. Sapiro, T. S. Huang, and S. Yan, “Sparse representation for computer vision and pattern recognition,” Proc. IEEE 98, 1031–1044 (2010). [CrossRef]
  5. J.-L. Starck, F. Murtagh, and J. M. Fadili, Sparse Image and Signal Processing (Cambridge University, 2010).
  6. E. Candès and M. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008). [CrossRef]
  7. J. Romberg, “Imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 14–20 (2008). [CrossRef]
  8. R. Baraniuk, “More is less: signal processing and the data deluge,” Science 331, 717–719 (2011). [CrossRef]
  9. Z. Xu and E. Y. Lam, “Image reconstruction using spectroscopic and hyperspectral information for compressive terahertz imaging,” J. Opt. Soc. Am. A 27, 1638–1646 (2010). [CrossRef]
  10. A. Fannjiang and H.-C. Tseng, “Compressive imaging of subwavelength structures: periodic rough surfaces,” J. Opt. Soc. Am. A 29, 617–626 (2012). [CrossRef]
  11. J. Bobin, J.-L. Stack, and R. Ottensamer, “Compressed sensing in astronomy,,” IEEE J. Sel. Top. Signal Process. 2, 718–726 (2008). [CrossRef]
  12. E. Candès, Y. Eldar, D. Needell, and P. Randall, “Compressed sensing with coherent and redundant dictionaries,” Appl. Comput. Harmon. Anal. 31, 59–73 (2011). [CrossRef]
  13. J. Bowley and L. Rebollo-Neira, “Sparsity and something else: an approach to encrypted image folding,” IEEE Signal Process. Lett. 18, 189–192 (2011). [CrossRef]
  14. L. Rebollo-Neira, J. Bowley, A. Constantinides, and A. Plastino, “Self contained encrypted image folding,” Phys. A 391, 5858–5870 (2012). [CrossRef]
  15. http://http://www.eso.org/public/ .
  16. http://hubblesite.org/ .
  17. R. Young, An Introduction to Nonharmonic Fourier Series(Academic, 1980).
  18. S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comput. 20, 33–61 (1998). [CrossRef]
  19. S. G. Mallat and Z. Zhang, “Matching pursuits with time-frequency dictionaries,” IEEE Trans. Signal Process. 41, 3397–3415 (1993). [CrossRef]
  20. L. K. Jones, “On a conjecture of Huber concerning the convergence of projection pursuit regression,” Ann. Statist. 15, 880–882 (1987). [CrossRef]
  21. Y. C. Pati, R. Rezaiifar, and P. S. Krishnaprasad, “Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition,” in Proceedings of 27th Asilomar Conference on Signals, Systems and Computers (IEEE, 1993), pp. 40–44.
  22. M. Andrle and L. Rebollo-Neira, “Cardinal B-spline dictionaries on a compact interval,” Appl. Comput. Harmon. Anal. 18, 336–346 (2005). [CrossRef]
  23. L. Rebollo-Neira and Z. Xu, “Sparse signal representation by adaptive non-uniform B-spline dictionaries on a compact interval,” Signal Process. 90, 2308–2313 (2010). [CrossRef]
  24. C. de Boor, A Practical Guide to Splines Applied Mathematical Sciences, Vol. 27 (Springer-Verlag, 1978).
  25. L. Rebollo-Neira and D. Lowe, “Optimized orthogonal matching pursuit approach,” IEEE Signal Process. Lett. 9, 137–140 (2002). [CrossRef]
  26. M. Andrle and L. Rebollo-Neira, “A swapping-based refinement of orthogonal matching pursuit strategies,” Signal Process. 86, 480–495 (2006). [CrossRef]
  27. http://www.nonlinear-approx/info .
  28. Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004). [CrossRef]
  29. I. Daubechies, Ten Lectures on Wavelets (SIAM, 1992).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited