Understanding NMR [formula omitted] spectral uncertainty

Abstract

NMR relaxation and diffusion data analysis commonly uses a wide range of methods from simple exponential fitting to Laplace inversions. The pros and cons of these methods are often the subject of intense debate. We show that the ill-conditioned nature of such analysis gives rise to a range of solutions for every method resulting in uncertainty in the spectral solution. Such uncertainty is in fact characteristic of the inversion method. We show a simple method of sparse spectral representation can be used to improve the statistics of multiple-exponential-based inversion schemes.