Efficient method for recovering the optimal unbiased linear spectrum-estimate from Hadamard transform spectrometers having nonideal masks

T. W. Johnson, Jin Bae Park, S. A. Dyer, B. K. Harms, R. A. Dyer

Research output: Contribution to journalArticle

15 Citations (Scopus)

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(log2 + 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.

Original languageEnglish
Pages (from-to)746-750
Number of pages5
JournalApplied Spectroscopy
Volume43
Issue number5
DOIs
Publication statusPublished - 1989 Jan 1

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Hadamard transforms
Spectrometers
Masks
masks
spectrometers
Recovery
estimates
Spectral resolution
recovery
spectral resolution

All Science Journal Classification (ASJC) codes

  • Instrumentation
  • Spectroscopy

Cite this

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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(log2 + 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.",
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Efficient method for recovering the optimal unbiased linear spectrum-estimate from Hadamard transform spectrometers having nonideal masks. / Johnson, T. W.; Park, Jin Bae; Dyer, S. A.; Harms, B. K.; Dyer, R. A.

In: Applied Spectroscopy, Vol. 43, No. 5, 01.01.1989, p. 746-750.

Research output: Contribution to journalArticle

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AU - Park, Jin Bae

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AU - Dyer, R. A.

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N2 - 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(log2 + 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.

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