On the Estimation of Magnetic Resonance Spectra Using Various Methods

Magnetic resonance spectroscopy (MRS) is emerging as a unique method of performing non-invasive metabolic assays on patients. The data obtained by these assays take the form of spectra which vary as a function of the chosen nucleus of interest. The fast Fourier transform (FFT) is the most direct and numerically efficient method for converting time-domain data to the frequency-domain. Depending on the nature of the original signal, it may be necessary to perform corrections to the data after the FFT. The corrections are needed as a consequence of doing the transformation on data which has noise and windowing errors associated with it. Windowing errors, in this context, refer to erroneous assumptions regarding the behavior of the data outside of the sampling window. The FFT assumes that the data inside of the sampling window represents at least one cycle of a periodic function, and that the window outside of the sampling window represents more cycles of the same periodic function. It will be shown that applying time series estimation to spectral estimation minimizes the effects of noise and sampling errors associated with the data by constructing a model of the original signal. Transforming this model gives better resolution, eliminates phase errors, and eliminates digitization uncertainty which would be associated with sampled data. This paper compares the efficacy of Prony\u27s method, different auto-regressive modeling techniques, and the Fourier transform on MRS data and proposes a best method for performing spectroscopic analysis