Bayesian signal extraction from noisy FT NMR spectra

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Abstract
The statistical interpretation of the histogram representation of NMR spectra is described, leading to an estimation of the probability density function of the noise. The white-noise and Gaussian hypotheses are discussed, and a new estimator of the noise standard deviation is derived from the histogram strategy. The Bayesian approach to NMR signal detection is presented. This approach homogeneously combines prior knowledge, obtained from the histogram strategy, together with the posterior information resulting from the test of presence of a set of reference shapes in the neighbourhood of each data point. This scheme leads to a new strategy in the local detection of NMR signals in 2D and 3D spectra, which is illustrated by a complete peak-picking algorithm.