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Applied Spectroscopy

Applied Spectroscopy

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  • Vol. 43, Iss. 5 — May. 1, 1989
  • pp: 746–750

An Efficient Method for Recovering the Optimal Unbiased Linear Spectrum-Estimate from Hadamard Transform Spectrometers Having Nonideal Masks

T. W. Johnson, J. B. Park, S. A. Dyer, B. K. Harms, and R. A. Dyer

Applied Spectroscopy, Vol. 43, Issue 5, pp. 746-750 (1989)


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Abstract

A spectrum-recovery method is presented which efficiently computes an optimal unbiased linear spectrum-estimate for measurements obtained with Hadamard transform (HT) spectrometers having nonideal masks. This method has the following advantages over other spectrum-recovery techniques: it is computationally efficient, it requires no additional measurements, and it computes an optimal spectrum-estimate. In the method presented, after the mask of the HT spectrometer has been characterized, approximately 3N preliminary arithmetic operations are performed once for a given spectrometer, where N is both the number of spectral resolution-elements desired and the number of measurements required. Each spectrum-estimate to be recovered then requires only an additional O[N(log2N + 4)] arithmetic operations. In contrast, conventional methods for obtaining an optimal unbiased linear spectrum-estimate require O(N3) preliminary operations, and O(2N2) operations during each spectrum-recovery.

Citation
T. W. Johnson, J. B. Park, S. A. Dyer, B. K. Harms, and R. A. Dyer, "An Efficient Method for Recovering the Optimal Unbiased Linear Spectrum-Estimate from Hadamard Transform Spectrometers Having Nonideal Masks," Appl. Spectrosc. 43, 746-750 (1989)
http://www.opticsinfobase.org/as/abstract.cfm?URI=as-43-5-746

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