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Chi-squared-based filters for high-fidelity signal-to-noise ratio enhancement of spectra

TitleChi-squared-based filters for high-fidelity signal-to-noise ratio enhancement of spectra
Publication TypeJournal Article
Year of Publication2008
AuthorsSchulze, HG, Foist, RB, Ivanov, A, Turner, RFB
JournalApplied Spectroscopy
Date PublishedAug
Type of ArticleArticle
ISBN Number0003-7028
Keywordschi(2)-based regularization, DECONVOLUTION, ENTROPY REGULARIZATION METHOD, noise reduction, Savitzky-Golay filters, Signal-to-noise ratio enhancement, SNR, spectral smoothing

When reconstructing a measured spectrum to enhance its signal-to-noise ratio (SNR), the objective is to minimize the variance between the smooth reconstructed spectrum and the original measured spectrum, hence to attain an acceptably small chi(2) value. The chi(2) value thus measures the fidelity of the reconstruction to the original. Smoothness can be conceived as attenuated variation between adjacent points in a spectrum. Thus, a conceptual change in the application of the chi(2) function to the difference between adjacent points of the reconstructed spectrum permits its use, in principle, as both a measure of smoothness and a measure of fidelity. We show here that implementations of this concept produce results superior to Savitzky-Golay filters.

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