An algorithm for discovery and determination of exponentially decaying components in nuclear magnetic resonance relaxometry data

In many branches of physics, the time evolution of various quantities measured in systems passing from excited to equilibrium states, while theoretically very complex, can be in practice well approximated by a sum of exponential decays. Multiexponential relaxometry data analysis is about determining the number of exponential components and their corresponding amplitudes and decay rates, starting from noisy recorded time series, under the assumption of the discreteness of the number of components present. A technique for decomposing a signal modelled as a sum of exponential decays into its components is introduced, consisting of a modified version of the algorithm minimum description length (MDL) + matrix pencil, originally proposed by Lin et al. for the analysis of nuclear magnetic resonance spectroscopy data. The procedure starts by denoising the discrete time-domain signal, and then a number of different decimations are applied, each being followed by an MDL + matrix pencil detection-estimation step, and finally, a postprocessing of the intermediate outcomes is done. The comprised model order estimator eliminates the need of providing prior estimates of the number of components present.