Maximum likelihood estimation of poles, amplitudes and phases from 2-D NMR time domain signals

For analytical purposes, it is often required to quantify a 2-D MR (magnetic resonance) signal in terms of physically relevant model parameters. To this end, the authors fit a sum of exponentially damped 2-D sinusoids to the data. It is shown that this approach can accommodate a full 2-D amplitude matrix as well as unequal numbers of signal poles in the two dimensions. Specifically, it is demonstrated that the numbers of signal poles in the two dimensions, K and K", need not be equal, and that all K×K" elements of the amplitude matrix are allowed to be nonzero. The authors treat two fundamentally different approaches for retrieving the desired model parameters from the data: a singular value decomposition approach and decomposition by the VARPRO method. Results of quantification of noise-corrupted simulated data are given