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3.3.2 Statistical Models for FT/UV Spectral Estimation

Mark Levenson
Statistical Engineering Division, ITL

Marc Salit, John Travis
Analytical Chemistry Division, CSTL

Judy Devaney
High Performance Systems and Services Division, ITL

Fourier transform spectrometry in the UV range (FT/UV) offers NIST the potential to significantly further its chemical measurement services. However, certain statistical and computational hurdles must be overcome to realize the full potential of FT/UV to NIST and the chemical community. NIST is well suited in personnel and facilities to overcome these hurdles.

In FT/UV, the chemical spectrum of interest is related to the instrument measurements through the Fourier transform. Typically, the Fast Fourier Transform (FFT) is used to estimate the spectrum. However, the instrument noise is not white, but Poisson. The FFT is only optimal in the white noise case. In the presence of Poisson noise, the noise from large peaks is spread out over the estimated spectrum, hiding smaller peaks. In an attempt to overcome this problem, a solution based on maximum likelihood and the EM algorithm has been proposed in the literature.

Working as a team of members across laboratories and divisions, we are developing statistical models and algorithms that correctly handle the Poisson noise and the sparse nature of the spectra. In particular, we are exploring the use of Iteratively Reweighted Least Squares (IRLS), which promises to converge much faster than the EM algorithm. Additionally, we are developing a parametric model of the spectral peaks. The FFT and the existing ML approaches are effectively non-parametric in that they estimate parameters for millions peaks. It is known that only around 10,000 peaks are possible. The use of this knowledge with correct statistical models may drastically improve accuracy and computational efficiency.

The accompanying figure shows how the noise can mask a peak in the spectrum, when using the FFT. The figure shows the FFT of a simulated instrument measurement. There are three peaks with magnitudes of 1600, 32, and 800, respectively, in the spectrum. The points show the FFT estimates and x's show the true magnitudes. The two large peaks are clearly distinguishable. However, the small peak does not stand out from the noise.

\epsfig{file=/proj/sedshare/panelbk/2000/data/projects/dex/,width=6.0in} \end{figure}

Figure 11: Results from preliminary simulation study.

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Date created: 7/20/2001
Last updated: 7/20/2001
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