Signal Deconvolution and Noise Factor Analysis Based on a Combination of Time–Frequency Analysis and Probabilistic Sparse Matrix Factorization

Nuclear magnetic resonance (NMR) spectroscopy is commonly used to characterize molecular complexity because it produces informative atomic-resolution data on the chemical structure and molecular mobility of samples non-invasively by means of various acquisition parameters and pulse programs. However, analyzing the accumulated NMR data of mixtures is challenging due to noise and signal overlap. Therefore, data-cleansing steps, such as quality checking, noise reduction, and signal deconvolution, are important processes before spectrum analysis. Here, we have developed an NMR measurement informatics tool for data cleansing that combines short-time Fourier transform (STFT; a time–frequency analytical method) and probabilistic sparse matrix factorization (PSMF) for signal deconvolution and noise factor analysis. Our tool can be applied to the original free induction decay (FID) signals of a one-dimensional NMR spectrum. We show that the signal deconvolution method reduces the noise of FID signals, increasing the signal-to-noise ratio (SNR) about tenfold, and its application to diffusion-edited spectra allows signals of macromolecules and unsuppressed small molecules to be separated by the length of the T(2)* relaxation time. Noise factor analysis of NMR datasets identified correlations between SNR and acquisition parameters, identifying major experimental factors that can lower SNR.