Improving resolution of miniature spectrometers by exploiting sparse nature of signals

doi:10.1364/OE.20.002613

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

View Full Text Article

Enhanced HTML Acrobat PDF (1482 KB)

Journal Search
Article Lookup

Article Tools

Citations

Alert me when this article is cited
Export Citation/Save

Abstract
Article Info
References (22)
Cited By
Figures (7)
Metrics
Related Content

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.

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

Sort: Author | Year | Journal | Reset

References

D. J. Brady, Optical Imaging and Spectroscopy, (John Wiley and Sons, 2009).
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]
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]
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]
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]
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]
H. N. Lee, Introduction to Compressed Sensing (Lecture notes; Spring Semester, GIST, South Korea, 2011).
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]
H. Chen and H. Tang, “Application of miniature spectrometer in liquid signature analysis technology,” Appl. Opt.50(26), 5093–5098 (2011). [CrossRef] [PubMed]
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.
S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM Rev.43(1), 129–159 (2001). [CrossRef]
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).
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]
D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory52, 1289–1306 (2006).
R. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag.24(4), 118–121 (2007). [CrossRef]
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).
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]
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).
J. A. Tropp, “Just relax: Convex programming methods for identifying sparse signals,” IEEE Trans. Inf. Theory52, 1030–1051 (2006).
S. Boyd and L. Vandenberghe, Convex Optimization, (Cambridge University Press, 2009).
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).
A. Forsgren, P. E. Gill, and M. H. Wright, “Interior methods for nonlinear optimization,” SIAM Rev.44(4), 525–597 (2002). [CrossRef]

Appl. Opt.

H. Chen and H. Tang, “Application of miniature spectrometer in liquid signature analysis technology,” Appl. Opt.50(26), 5093–5098 (2011). [CrossRef] [PubMed]

Commun. Pure Appl. Math.

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]

Food Chem.

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]

IEEE J. Sel. Top. Signal Process.

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).

IEEE Sens. J.

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]

IEEE Signal Process. Mag.

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]
R. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag.24(4), 118–121 (2007). [CrossRef]

IEEE Trans. Inf. Theory

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).
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).
J. A. Tropp, “Just relax: Convex programming methods for identifying sparse signals,” IEEE Trans. Inf. Theory52, 1030–1051 (2006).
D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory52, 1289–1306 (2006).

Opt. Eng.

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]

Opt. Express

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]

Opt. Lett.

Proc. SPIE

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).

SIAM Rev.

A. Forsgren, P. E. Gill, and M. H. Wright, “Interior methods for nonlinear optimization,” SIAM Rev.44(4), 525–597 (2002). [CrossRef]
S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM Rev.43(1), 129–159 (2001). [CrossRef]

Other

S. Boyd and L. Vandenberghe, Convex Optimization, (Cambridge University Press, 2009).
D. J. Brady, Optical Imaging and Spectroscopy, (John Wiley and Sons, 2009).
H. N. Lee, Introduction to Compressed Sensing (Lecture notes; Spring Semester, GIST, South Korea, 2011).
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.

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.

Click here to see a list of articles that cite this paper

Figures


Fig. 1	Fig. 2	Fig. 3


Fig. 4	Fig. 5	Fig. 6


Fig. 7

« Previous Article | Next Article »

OSA is a member of CrossRef.

[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]

OpticsInfoBase

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

Improving resolution of miniature spectrometers by exploiting sparse nature of signals