JOURNAL OF MAGNETIC RESONANCE 83,586-594 (1989) NOTES Application of the Maximum Likelihood Method to a Large 2D NMR Spectrum Using a Parallel Computer R. E. HOFFMAN, A. KUMAR, K. D. BISHOP, P. N. BORER, AND G. C. LEVY* NIH Resource, Northeast Parallel Architectures Center (NPAC), and Chemistry Department, Centerfor Science and Technology, Syracuse University. Syracuse, New York 13244-4100 Received July 25,1988; revised November 18, 1988 The maximum likelihood method (MLM) suppresses noise in two-dimensional spectra while keeping the time-domain data within certain statistical limits. It is an iterative method which in the implementation used in this work (I) requires three Fourier transforms per iteration and is based on the method proposed by J. Capon (2), originally applied to 2D NMR by F. Ni. In contrast to the maximum entropy method (MEM), the MLM algorithm requires fewer computations per iteration and is therefore potentially faster. Each iteration is less complicated because logarithm calculations and diagonalization of metric ten- sors are not required (3). However, the two algorithms differ in their basic assump- tions. In the MLM algorithm, the best fit is obtained by minimizing the variance computed by the sum of the weighted squared differences between the time-domain data and its estimate; i.e., the entropy is not maximized. The results of 2D MLM are similar to those reported for 2D MEM: increased reso- lution, increased apparent signal-to-noise, and loss of phase information (4,5). MLM does not distort the position of lines and as with most resolution-enhancement tech- niques, it tends to correct distortions caused by peak overlap. Initial results show that the accuracy of integrated intensities measured by MLM is comparable to or better than those measured by conventional Fourier transform processing. It has been found that it is not possible to isolate signals with MLM that are too weak to be observed at all by conventional means. Therefore, as previously reported for MEM (6-10) and minimum-area reconstructed spectra (MARS) (I 1) the increase in signal-to-noise is only apparent (a dramatic contrast enhancement) and noise is preferentially suppressed where there are no signals. MLM is still useful for an unbi- ased assessment of what is and what is not noise, and, in particular, for highly com- plex 2D NMR spectra, MLM can significantly enhance visualization of weak cross peaks. Such assessments can never be perfect, but the few spurious signals that arise can be detected as they are unlikely to occur on both sides of the diagonal in the case of a 2D NOESY spectrum. MLM is therefore expected to be of most value as an aid to automated spectral assignments. * To whom correspondence shouldbe addressed. 0022-2364189 $3.00 586 Copyright 43 1989 by Academic Press, Inc. AU rights of reproduction in any form rrsenred.