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-matrix formalism for quantitative noise assessment of covariance nuclear magnetic resonance spectra
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10.1063/1.2975206
/content/aip/journal/jcp/129/10/10.1063/1.2975206
http://aip.metastore.ingenta.com/content/aip/journal/jcp/129/10/10.1063/1.2975206

Figures

Image of FIG. 1.
FIG. 1.

Signal-to-noise (S∕N) ratio of a peak arising from the covariance of a pair of peaks, computed using Eq. (9) as a function of and the S∕N ratio of the input peaks. (a) S∕N for the covariance between peaks each having the indicated (5, 10, and 20) S∕N values. (b) S∕N for the covariance between a peak with and a peak with the indicated S∕N. Note that the lower the signal to noise of the weaker peak, the lower the signal to noise of the covariance peak. However, in the limit where the weaker peak is much weaker than the stronger peak, so long as is small, the signal to noise of the covariance peak approaches that of the weaker peak. The sensitivity of an unsymmetric covariance spectrum, for small values of , is not that much lower than that of the less sensitive of the two spectra subject to covariance with signal-to-noise values decreasing at most by a factor from that of the least sensitive of the two input spectra.

Image of FIG. 2.
FIG. 2.

Noise propagation through unsymmetric covariance. (a) Simulated (noisy) input spectrum with . (b) Covariance spectrum , where has the same signal peak as and the same noise level. (c) The variance calculated using Eq. (10) at each point of the covariance spectrum. (d) matrix calculated according to Eq. (11). (e) same as (d) after setting all elements to zero with a S∕N ratio less than (4.85), the score belonging to the critical value for which Dunn–Sidak correction yields a spectrum-wide . (f) The covariance spectrum produced by thresholding by setting all elements of and less than to zero prior to covariance. In (a), (b), (d), (e), and (f) the cross peak is truncated to highlight noise features: the actual peak heights are 44, 2112, 33, 33, and 2101, respectively.

Image of FIG. 3.
FIG. 3.

Covariance of simulated spectra (as described in text) subjected to maxima ratio scaling (mrs). The peak is truncated and has an actual height of 2059.

Image of FIG. 4.
FIG. 4.

Noise propagation through unsymmetric covariance. (a) Simulated input spectrum A as in Fig. 2 with . (b) Covariance spectrum , where has the same signal peak as and the same noise level. (c) matrix calculated according to Eq. (11). (d) same as (c) after setting all elements to zero with a S∕N ratio less than (4.85), cf. Fig. 2. (e) The covariance spectrum produced by thresholding by setting all elements of and less than to zero prior to covariance. (f) Covariance of simulated spectra subjected to maxima ratio scaling (mrs). In each panel, the cross peak is truncated to highlight noise features: the actual peak heights are 48, 2387, 5, 5, 2170, and 2246, respectively.

Image of FIG. 5.
FIG. 5.

Selected spectral region taken from an experimental unsymmetric HSQC-HMBC covariance spectrum of metabolite mixture using different processing schemes. (a) Covariance spectrum computed according to Eq. (1). (b) The variance calculated, by Eq. (10) at each point in the covariance spectrum. (c) matrix calculated according to Eq. (11). (d) as (c), after setting all elements to zero having a S∕N ratio less than (5.85), the score belonging to the critical value for which Dunn–Sidak correction yields a spectrum-wide . (e) Spectrum computed using thresholding at applied to the input HMBC and HSQC spectra. (f) Spectrum computed using maxima ratio scaling according to Eqs. (13) and (14). In (a), (c), (d), (e), and (f), the cross peak (corresponding to peak 2 in text and tables) has been clipped: the maximum amplitude of this peak is 263 [(a) and (e)], 294 [(c) and (d)], and 144 (f).

Tables

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Table I.

Variance of noise intensities in a simple unsymmetric covariance spectrum: simulation vs theory.

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Table II.

Variances of column∕row noise and peak intensity for two covariance peaks.

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Table III.

Expected signal-to-noise ratios for two covariance peaks.

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/content/aip/journal/jcp/129/10/10.1063/1.2975206
2008-09-10
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Z-matrix formalism for quantitative noise assessment of covariance nuclear magnetic resonance spectra
http://aip.metastore.ingenta.com/content/aip/journal/jcp/129/10/10.1063/1.2975206
10.1063/1.2975206
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