The CORE method
CORE stands for COmponent-REsolved [spectroscopy]. It is a general data processing tool that allows one to fully extract bandshapes and decay rates from spectral data sets of a 'kinetic type'. CORE processing was originally developed for Fourier Transform Pulsed-Gradient Spin-Echo (FT-PGSE) NMR data sets.
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The basic method is described in two publications; P.Stilbs, K.Paulsen and P.C. Griffiths, J. Phys. Chem. 100 (1996) 8180-8189 and P.Stilbs and K.Paulsen, Rev. Sci. Instrum., 67 (1996) 4380-4386. CORE processing has also been applied to 2-dimensional data in the form of images (P. Stilbs, J. Magn. Reson., 135 (1998) 236-241).
CORE processing is based on a simple, global, least-squares approach, using a two-level minimization scheme. No assumptions whatsoever are made with regard to component bandshapes - the iteration is made on the (global) kinetic rate constants of the data set only.
This is a typical spectral data set. It happens to have three components; two exponentially decaying, and one exponentially evolving. The respective rate constants differ by a factor of two.
The next picture shows the same original data, the global fit, the residual map and the extracted components.The extracted rate constants agree within 1% with those the simulated data were based upon, before adding artificial Gaussian noise.
