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