Determining the number of chemical species in nuclear magnetic resonance data matrix by taking advantage of collinearity and noise

The number of chemical species is crucial in analyzing pulsed field gradient nuclear magnetic resonance spectral data. Any method to determine the number must handle the obstacles of collinearity and noise. Collinearity in pulsed field gradient NMR data poses a serious challenge to and fails many existing methods. A novel method is proposed by taking advantage of the two obstacles instead of eliminating them. In the proposed method, the determination is based on discriminating decay-profile-dominant eigenvectors from noise-dominant ones, and the discrimination is implemented with a novel low- and high-frequency energy ratio (LHFER). Its performance is validated with both simulated and experimental data. The method is mathematically rigorous, computationally efficient, and readily automated. It also has the potential to be applied to other types of data in which collinearity is fairly severe.