A Method for Analyzing Data from 1- and 2-Dimensional Relaxation and Diffusion NMR Experiments by Determination of their Expectation Values and Standard Deviations

Abstract A method for analyzing ill-posed multi-exponentially decaying data from 1- and 2-Dimensional experiments by Determination of the Expectation Values and their Standard Deviation has been developed. It combines a repeated use of the discrete Anahess approach for analyzing the dynamic data where a regrouping of the noise in the data is performed for each repetition. These resulting expectation values are used as initial and restricting values to produce a distribution using the Inverse Laplace transform, where position and volume of the distribution can then be reported with expectation value and standard deviation. The method is verified on synthetic data and tested on real data in both one and two dimensions.