High dynamic-range magnetic resonance spectroscopy (MRS) time-domain signal analysis

In the absence of water signal suppression, the proton magnetic resonance spectroscopy (¹H MRS) in vivo water resonance signal-to-noise ratio (SNR) is orders of magnitude larger than the SNR of all the other resonances. In this case, because the high-SNR water resonance dominates the data, it is difficult to obtain reliable parameter estimates for the low SNR resonances. Herein, a new model is described that offers a solution to this problem. In this model, the time-domain signal for the low SNR resonances is represented as the conventional sum of exponentially decaying complex sinusoids. However, the time-domain signal for the high SNR water resonance is assumed to be a complex sinusoid whose amplitude is slowly varying from pure exponential decay and whose phase is slowly varying from a constant frequency. Thus, the water resonance has only an instantaneous amplitude and frequency. The water signal is neither filtered nor subtracted from the data. Instead, Bayesian probability theory is used to simultaneously estimate the frequencies, decay-rate constants, and amplitudes for all the low SNR resonances, along with the water resonance's time-dependent amplitude and phase. While computationally intensive, this approach models all of the resonances, including the water and the metabolites of interest, to within the noise level.