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. 6 — Jun. 1, 2013
  • pp: 1069–1077

Quantization error and dynamic range considerations for compressive imaging systems design

Adrian Stern, Yigal Zeltzer, and Yair Rivenson  »View Author Affiliations


JOSA A, Vol. 30, Issue 6, pp. 1069-1077 (2013)
http://dx.doi.org/10.1364/JOSAA.30.001069


View Full Text Article

Enhanced HTML    Acrobat PDF (536 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A natural field of application for compressive sensing theory is imaging. Indeed, numerous compressive imaging (CI) systems and applications have been developed during the last few years. This work addresses the quantization effect in CI, which is fundamental for most CI architectures. In this paper, the implications of sensor quantization on universal CI are investigated theoretically and demonstrated with numerical experiments. It is shown that employing a CI framework may set severe requirements on the quantization depth of the optical sensor used. The quantization depth overhead requirement may be prohibitive in many optical imaging scenarios employing typical CI architectures. Practical solutions that significantly alleviate this requirement are suggested.

© 2013 Optical Society of America

OCIS Codes
(110.4280) Imaging systems : Noise in imaging systems
(110.1758) Imaging systems : Computational imaging

ToC Category:
Imaging Systems

History
Original Manuscript: December 21, 2012
Revised Manuscript: March 10, 2013
Manuscript Accepted: April 7, 2013
Published: May 8, 2013

Citation
Adrian Stern, Yigal Zeltzer, and Yair Rivenson, "Quantization error and dynamic range considerations for compressive imaging systems design," J. Opt. Soc. Am. A 30, 1069-1077 (2013)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-6-1069


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006). [CrossRef]
  2. E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006). [CrossRef]
  3. D. Takhar, J. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).
  4. W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008). [CrossRef]
  5. C. F. Cull, D. A. Wikner, J. N. Mait, M. Mattheiss, and D. J. Brady, “Millimeter-wave compressive holography,” Appl. Opt. 49, E67–E82 (2010). [CrossRef]
  6. A. Stern, “Compressed imaging system with linear sensors,” Opt. Lett. 32, 3077–3079 (2007). [CrossRef]
  7. A. Stern and B. Javidi, “Random projections imaging with extended space-bandwidth product,” J. Display Technology 3, 315–320 (2007). [CrossRef]
  8. S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse sub-wavelength images: erratum,” Opt. Express 17, 23920–23946 (2009). [CrossRef]
  9. Y. Shechtman, S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse images carried by incoherent light,” Opt. Lett. 35, 1148–1150 (2010). [CrossRef]
  10. Y. Rivenson, A. Stern, and B. Javidi, “Single exposure super-resolution compressive imaging by double phase encoding,” Opt. Express 18, 15094–15103 (2010). [CrossRef]
  11. Y. Kashter, O. Levi, and A. Stern, “Optical compressive change and motion detection,” Appl. Opt. 51, 2491–2496 (2012). [CrossRef]
  12. D. Townsend, P. Poon, S. Wehrwein, T. Osman, A. Mariano, E. Vera, M. Stenner, and M. Gehm, “Static compressive tracking,” Opt. Express 20, 21160–21172 (2012). [CrossRef]
  13. Y. Rivenson, A. Rot, S. Balber, A. Stern, and J. Rosen, “Recovery of partially occluded objects by applying compressive Fresnel holography,” Opt. Lett. 37, 1757–1759 (2012). [CrossRef]
  14. A. Ú. Bourquard, F. Aguet, and M. Unser, “Optical imaging using binary sensors,” Opt. Express 18, 4876–4888 (2010). [CrossRef]
  15. R. Horisaki, K. Choi, J. Hahn, J. Tanida, and D. J. Brady, “Generalized sampling using a compound-eye imaging system for multi-dimensional object acquisition,” Opt. Express 18, 19367–19378 (2010). [CrossRef]
  16. R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. 50, 072601 (2011). [CrossRef]
  17. E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59, 1207–1223 (2006). [CrossRef]
  18. E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008). [CrossRef]
  19. D. J. Brady, Optical Imaging and Spectroscopy (Wiley-Interscience, 2009).
  20. M. A. Neifeld and J. Ke, “Optical architectures for compressive imaging,” Appl. Opt. 46, 5293–5303 (2007). [CrossRef]
  21. W. L. Chan, M. L. Moravec, R. G. Baraniuk, and D. M. Mittleman, “Terahertz imaging with compressed sensing and phase retrieval,” Opt. Lett. 33, 974–976 (2008). [CrossRef]
  22. J. Gu, S. Nayar, E. Grinspun, P. Belhumeur, and R. Ramamoorthi, “Compressive structured light for recovering inhomogeneous participating media,” in Computer Vision–ECCV,” Vol. 5305 of Lecture Notes in Computer Science (Springer, 2008), pp. 845–858.
  23. F. Magalhães, F. M. Araújo, M. V. Correia, M. Abolbashari, and F. Farahi, “Active illumination single-pixel camera based on compressive sensing,” Appl. Opt. 50, 405–414 (2011). [CrossRef]
  24. R. F. Marcia, Z. T. Harmany, and R. M. Willett, “Compressive coded aperture imaging,” Proc. SPIE 7246, 72460G (2009).
  25. R. Horisaki, J. Tanida, A. Stern, and B. Javidi, “Multidimensional imaging using compressive Fresnel holography,” Opt. Lett. 37, 2013–2015 (2012). [CrossRef]
  26. J. Ke and E. Y. Lam, “Object reconstruction in block-based compressive imaging,” Opt. Express 20, 22102–22117 (2012). [CrossRef]
  27. M. Cho, A. Mahalanobis, and B. Javidi, “3D passive integral imaging using compressive sensing,” Opt. Express 20, 26624–26635 (2012). [CrossRef]
  28. J. M. Bioucas-Dias, and M. A. T. Figueiredo, “A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16, 2992–3004 (2007). [CrossRef]
  29. A. M. Bruckstein, M. Elad, and M. Zibulevsky, “On the uniqueness of nonnegative sparse solutions to underdetermined systems of equations,” IEEE Trans. Inf. Theory 54, 4813–4820 (2008). [CrossRef]
  30. M. Wang, W. Xu, and A. Tang, “A unique “nonnegative” solution to an underdetermined system: from vectors to matrices,” IEEE Trans. Signal Process. 59, 1007–1016 (2011). [CrossRef]

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