Parallel Algorithms for Maximum-Likelihood Nuclear Magnetic Resonance Spectroscopy

Abstract

Using the free-induction-decay signal model of one-dimensional nuclear magnetic resonance signals, maximum-likelihood (ML) methods for one-dimensional NMR spectroscopy are developed. The ML method distinguishes signal from noise in the NMR spectrum by providing direct estimates of the NMR signal parameters. It is shown that the ML estimates of the frequencies and phase parameters of the FID models are unbiased, with the amplitudes and exponential decay parameters showing increasing bias with noise power. Methods to speed up the computation of the ML algorithm on parallel computers are developed, demonstrating that the class of single-instruction multiple-data-stream machines allows for parallelism on the order of the number of data points in the FID. The class of multiple-instruction multiple-data-stream machines affords parallelism at the level of the number of sinusoids in the FID.