Study of Uncertainties in the Inversion Algorithms for Transverse Relaxation Distribution

Nuclear magnetic resonance (NMR) relaxation spectrum is often used as fingerprints of molecular species, structure and dynamics in the study of complex multiphase system. Inversion algorithms such as singular value decomposition (SVD), Non-negative least square (NNLS), Solid iteration rebuild technique (SIRT) have been widely used in analyzing NMR data to obtain a T₁ or T₂ spectrum. However, due to the ill-conditioned nature of such inversion, it is difficult to determine the reliability of the inversion result. The concrete model is realized in MATLAB according the thought of the above three algorithms in this article. We converged to the true distribution by matching up the inversion spectrum from a series of true decay data collected from the NMR analyst instrument and a noisy simulated model, then evaluated the effects of noise in the original NMR data.