Lorentzian peak sharpening and sparse blind source separation for NMR spectroscopy

In this paper, we introduce a preprocessing technique for blind source separation of nonnegative and overlapped data. For nuclear magnetic resonance spectroscopy (NMR), the classical method Naanaa Nuzillard (NN) requires condition that signals to be non-overlapping at certain locations, while they are allowed overlap with each other elsewhere. NN’s works well data possess stand-alone peaks (SAPs). The SAP does not hold completely realistic NMR spectra, however. Violation often introduces errors or artifacts in results. To address issue, is developed here based on Lorentzian peak shapes weighted sharpening. idea superimpose original signal its negative second-order derivative. resulting sharpened (narrower taller) enable work more relaxed condition, so-called dominant deliver improved achieve an optimal sharpening preserving nonnegativity, prove existence upper bound weight parameter propose selection criterion. Numerical experiments show satisfactory performance our proposed method.