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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 7, Iss. 3 — Feb. 29, 2012

Improving resolution of miniature spectrometers by exploiting sparse nature of signals

J. Oliver, Woongbi Lee, Sangjun Park, and Heung-No Lee  »View Author Affiliations


Optics Express, Vol. 20, Issue 3, pp. 2613-2625 (2012)
http://dx.doi.org/10.1364/OE.20.002613


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Abstract

In this paper, we present a signal processing approach to improve the resolution of a spectrometer with a fixed number of low-cost, non-ideal filters. We aim to show that the resolution can be improved beyond the limit set by the number of filters by exploiting the sparse nature of a signal spectrum. We consider an underdetermined system of linear equations as a model for signal spectrum estimation. We design a non-negative L 1 norm minimization algorithm for solving the system of equations. We demonstrate that the resolution can be improved multiple times by using the proposed algorithm.

© 2012 OSA

OCIS Codes
(100.6640) Image processing : Superresolution
(120.6200) Instrumentation, measurement, and metrology : Spectrometers and spectroscopic instrumentation
(300.6320) Spectroscopy : Spectroscopy, high-resolution

ToC Category:
Spectroscopy

History
Original Manuscript: December 2, 2011
Revised Manuscript: January 4, 2012
Manuscript Accepted: January 5, 2012
Published: January 20, 2012

Virtual Issues
Vol. 7, Iss. 3 Virtual Journal for Biomedical Optics

Citation
J. Oliver, Woongbi Lee, Sangjun Park, and Heung-No Lee, "Improving resolution of miniature spectrometers by exploiting sparse nature of signals," Opt. Express 20, 2613-2625 (2012)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-20-3-2613


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References

  1. D. J. Brady, Optical Imaging and Spectroscopy, (John Wiley and Sons, 2009).
  2. S. W. Wang, X. Chen, W. Lu, L. Wang, Y. Wu, and Z. Wang, “Integrated optical filter arrays fabricated by using the combinatorial etching technique,” Opt. Lett.31(3), 332–334 (2006). [CrossRef] [PubMed]
  3. S. W. Wang, C. Xia, X. Chen, W. Lu, M. Li, H. Wang, W. Zheng, and T. Zhang, “Concept of a high-resolution miniature spectrometer using an integrated filter array,” Opt. Lett.32(6), 632–634 (2007). [CrossRef] [PubMed]
  4. C. C. Chang and H. N. Lee, “On the estimation of target spectrum for filter-array based spectrometer,” Opt. Express16(2), 1056–1061 (2008). [CrossRef]
  5. U. Kurokawa, B. I. Choi, and C.-C. Chang, “Filter-based miniature spectrometers: spectrum reconstruction using adaptive regularization,” IEEE Sens. J.11(7), 1556–1563 (2011). [CrossRef]
  6. C. C. Chang, N. T. Lin, U. Kurokawa, and B. I. I. Choi, “Spectrum reconstruction for filter-array spectrum sensor from sparse template selection,” Opt. Eng.50(11), 114402 (2011). [CrossRef]
  7. H. N. Lee, Introduction to Compressed Sensing (Lecture notes; Spring Semester, GIST, South Korea, 2011).
  8. H. Y. Yu, X. Y. Niu, H. J. Lin, Y. B. Ying, B. B. Li, and X. X. Pan, “A feasibility study on on-line determination of rice wine composition by Vis-NIR spectroscopy and least-squares support vector machines,” Food Chem.113(1), 291–296 (2009). [CrossRef]
  9. H. Chen and H. Tang, “Application of miniature spectrometer in liquid signature analysis technology,” Appl. Opt.50(26), 5093–5098 (2011). [CrossRef] [PubMed]
  10. N. J. Chanover, D. A. Glenar, D. G. Voelz, X. Xiao, R. Tawalbeh, P. J. Boston, W. B. Brinckerhoff, P. R. Mahaffy, S. Getty, I. Ten Kate, and A. McAdam, “An AOTF-LDTOF spectrometer suite for in situ organic detection and characterization,” in Proceedings of IEEE Aerospace Conference (2011), pp. 1–13.
  11. S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM Rev.43(1), 129–159 (2001). [CrossRef]
  12. D. L. Donoho, M. Elad, and V. Temlyakov, “Stable recovery of sparse over complete representations in the presence of noise,” IEEE Trans. Inf. Theory52, 6–18 (2006).
  13. D. L. Donoho, “For most large underdetermined systems of linear equations, the minimal l1-norm solution is also the sparsest near solution,” Commun. Pure Appl. Math.59, 907–934 (2006). [CrossRef]
  14. D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory52, 1289–1306 (2006).
  15. R. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag.24(4), 118–121 (2007). [CrossRef]
  16. D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE6065, 43–52 (2006).
  17. M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag.25(2), 83–91 (2008). [CrossRef]
  18. D. L. Dohono and Y. Tsaig, “Fast solution of L1-norm minimization problems when the solution may be sparse,” IEEE Trans. Inf. Theory54, 4789–4812 (2008).
  19. J. A. Tropp, “Just relax: Convex programming methods for identifying sparse signals,” IEEE Trans. Inf. Theory52, 1030–1051 (2006).
  20. S. Boyd and L. Vandenberghe, Convex Optimization, (Cambridge University Press, 2009).
  21. S. J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process.1, 606–617 (2007).
  22. A. Forsgren, P. E. Gill, and M. H. Wright, “Interior methods for nonlinear optimization,” SIAM Rev.44(4), 525–597 (2002). [CrossRef]

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