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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 19, Iss. 12 — Dec. 1, 2002
  • pp: 2495–2509

Analysis of spectroscopic measurements of leaf water content at terahertz frequencies using linear transforms

Sillas Hadjiloucas, Roberto K. H. Galvão, and John W. Bowen  »View Author Affiliations


JOSA A, Vol. 19, Issue 12, pp. 2495-2509 (2002)
http://dx.doi.org/10.1364/JOSAA.19.002495


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Abstract

We provide a unified framework for a range of linear transforms that can be used for the analysis of terahertz spectroscopic data, with particular emphasis on their application to the measurement of leaf water content. The use of linear transforms for filtering, regression, and classification is discussed. For illustration, a classification problem involving leaves at three stages of drought and a prediction problem involving simulated spectra are presented. Issues resulting from scaling the data set are discussed. Using Lagrange multipliers, we arrive at the transform that yields the maximum separation between the spectra and show that this optimal transform is equivalent to computing the Euclidean distance between the samples. The optimal linear transform is compared with the average for all the spectra as well as with the Karhunen–Loève transform to discriminate a wet leaf from a dry leaf. We show that taking several principal components into account is equivalent to defining new axes in which data are to be analyzed. The procedure shows that the coefficients of the Karhunen–Loève transform are well suited to the process of classification of spectra. This is in line with expectations, as these coefficients are built from the statistical properties of the data set analyzed.

© 2002 Optical Society of America

OCIS Codes
(010.7340) Atmospheric and oceanic optics : Water
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(100.7410) Image processing : Wavelets
(170.1580) Medical optics and biotechnology : Chemometrics
(300.6270) Spectroscopy : Spectroscopy, far infrared
(300.6300) Spectroscopy : Spectroscopy, Fourier transforms
(330.6180) Vision, color, and visual optics : Spectral discrimination
(350.6980) Other areas of optics : Transforms

Citation
Sillas Hadjiloucas, Roberto K. H. Galvão, and John W. Bowen, "Analysis of spectroscopic measurements of leaf water content at terahertz frequencies using linear transforms," J. Opt. Soc. Am. A 19, 2495-2509 (2002)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-19-12-2495


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