Maximum Entropy Spectral Reconstruction of Non-Uniformly Sampled Data

The time required to complete a multidimensional NMR experiment is directly proportional to the number of evolution times sampled in the indirect dimensions. A consequence when utilizing conventional methods of data acquisition and spectrum analysis is that resolution in the indirect dimensions is frequently sample-limited. The problem becomes more acute at very high magnetic fields, where increased chemical shift dispersion requires shorter time increments to avoid aliasing. It has long been recognized that a way to avoid this limitation is to utilize methods of spectrum analysis that do not require data to be sampled at uniform intervals, permitting the collection of data at long evolution times requisite for high resolution without requiring collection of data at all intervening multiples of the sampling interval. Several promising methods have evolved that are seemingly quite different, yet can be shown to yield similar results when applied to similar sampling strategies, emphasizing the importance of the choice of samples, regardless of the technique used to compute the spectrum. Maximum entropy (MaxEnt) reconstruction is a very general method for spectrum analysis of non-uniformly sampled data (NUS), and because it can be used with essentially arbitrary sampling strategies and makes no assumptions about the nature of the signal, it provides a convenient basis for exploring the influence of the choice of samples on spectral quality. In this article we use this versatility of MaxEnt reconstruction to compare different approaches to NUS in multidimensional NMR and suggest strategies for improving spectral quality by careful choice of sample times.