OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 24, Iss. 2 — Jan. 15, 1985
  • pp: 162–167

Superresolution of Fourier transform spectra by autoregressive model fitting with singular value decomposition

Keiichiroh Minami, Satoshi Kawata, and Shigeo Minami  »View Author Affiliations


Applied Optics, Vol. 24, Issue 2, pp. 162-167 (1985)
http://dx.doi.org/10.1364/AO.24.000162


View Full Text Article

Enhanced HTML    Acrobat PDF (682 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Autoregressive model fitting with singular value decomposition is applied to the interferogram data measured by a Fourier transform spectrometer to estimate superresolving spectra. The interferogram data matrix is decomposed into singular values with eigenvectors and its generalized inverse matrix is used for estimating the coefficients of the autoregressive model. This method suppresses the noise component in the data and avoids the risk of producing spurious peaks, which were the problem inherent in our earlier work using the maximum entropy method [ Appl. Opt. 22, 3593 ( 1983)]. The experimental results of superresolving spectral estimation are shown with the data of a visible emission spectrum and infrared absorption spectra.

© 1985 Optical Society of America

History
Original Manuscript: July 9, 1984
Published: January 15, 1985

Citation
Keiichiroh Minami, Satoshi Kawata, and Shigeo Minami, "Superresolution of Fourier transform spectra by autoregressive model fitting with singular value decomposition," Appl. Opt. 24, 162-167 (1985)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-24-2-162


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. L. Mertz, Transformations in Optics (Wiley, New York, 1965).
  2. J. L. Harris, “Diffraction and Resolving Power,” J. Opt. Soc. Am. 54, 931 (1964). [CrossRef]
  3. D. Slepian, H. O. Pollak, “Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty-I,” Bell Syst. Tech. J. 40, 43 (1961).
  4. R. W. Gerchberg, “Superresolution Through Error Energy Reduction,” Opt. Acta 21, 709 (1974). [CrossRef]
  5. A. Papoulis, “A New Algorithm in Spectral Analysis and Bandlimited Extrapolation,” IEEE Trans. Circuits Syst. CAS-22, 735 (1975). [CrossRef]
  6. J. Connes, “Resolution Enhancement by Numerical Methods,” presented at 1983 International Conference on Fourier Transform Spectroscopy, Durham U., U.K. (Sept. 1983).
  7. S. Kawata, K. Minami, S. Minami, “Superresolution of Fourier Transform Spectroscopy Data by the Maximum Entropy Method,” Appl. Opt. 22, 3593 (1983). [CrossRef] [PubMed]
  8. T. J. Ulrych, M. Ooe, “Autoregressive and Mixed Autoregressive-Moving Average Models and Spectra,” in Nonlinear Methods of Spectral Analysis, S. Haykin, Ed. (Springer, Berlin, 1979). [CrossRef]
  9. S. M. Kay, S. L. Marple, “Spectral Analysis—a Modern Perspective,” Proc. IEEE 69, 1380 (1981). [CrossRef]
  10. D. W. Tuft, R. Kumaresan, “Singular Value Decomposition and Improved Frequency Estimation Using Linear Prediction,” IEEE Trans. Acoust. Speech Signal Process. ASSP-30, 671 (1982). [CrossRef]
  11. C. R. Rao, S. K. Mitra, Generalized Inverse of Matrices and Its Applications (Wiley, New York, 1971).
  12. T. Okamoto, S. Kawata, S. Minami, “Fourier Transform Spectrometer with a Self-Scanning Photodiode Array,” Appl. Opt. 23, 269 (1984). [CrossRef] [PubMed]

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.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4 Fig. 5
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited