Variational Bayesian analysis of nonuniformly sampled NMR data

Abstract

Nonuniform sampling (NUS) offers NMR spectroscopists a means of accelerating data collection and increasing spectral quality in multidimensional (nD) experiments. The data from NUS experiments are incomplete by design, and must be reconstructed prior to use. While most existing reconstruction techniques compute point estimates of the true signal, Bayesian statistics offers a means of estimating posterior distributions over the signal, which enable more rigorous quantitation and uncertainty estimation. In this article, we describe the variational approach to approximating Bayesian posterior distributions, and illustrate how it can be applied to extend existing results from Bayesian spectrum analysis and compressed sensing. The new NUS reconstruction algorithms resulting from variational Bayes are computationally efficient, and offer new insights into the concepts of spectral sparsity and optimal sampling in NMR experiments.