Direct exponential curve resolution algorithm (DECRA): A novel application of the generalized rank annihilation method for a single spectral mixture data set with exponentially decaying contribution profiles

The generalized rank annihilation method (GRAM) is a powerful method for calibration and self-modeling curve resolution. The mathematical treatment requires two data sets, which implies two experiments. The required relation between the two data sets is strict and minor differences, such as in retention times for hyphenated techniques, violate the mathematical requirements leading to erroneous results. It will be shown in this paper that only one experiment is needed in the case where the contribution of the components in the mixture spectra is of a decaying exponential character. Examples are given of pulsed gradiet spin echo (PGSE) nuclear magnetic resonance (NMR) data. The MATLAB function to reproduce the results is given and is available through Chemolab's archives, together with the data files. The method is called DECRA (direct exponential curve resolution algorithm).