A mathematical assessment of the precision of parameters in measuring resonance spectra

The accurate interpretation of in vivo magnetic resonance spectroscopy (MRS ) spectra requires a complete understanding of the associated noise-induced errors, In this paper, we address the effect of complex correlated noise p atterns on the measurement of a set of peak parameters. This is examined in itially at the level of a single spectral analysis followed by addressing t he noise-induced errors associated with determining the signal parameters f rom the peak parameters. We describe a relatively simple method for calcula ting these errors for any correlated noise pattern in terms of the noise st andard deviation and correlation length. The results are presented in such a way that an estimate of the errors may be made from a single MRS spectrum . We also explore how, under certain circumstances, the lineshape of the si gnal may be determined. We then apply these results to reexamine a set of i n vivo P-31 MRS spectra obtained from rat brain prior to and following mode rate fluid percussion injury. The approach outlined in this paper will demo nstrate how meaningful results may be obtained from spectra where the signa l-to-noise ratio (SNR) is quite small and where knowledge of the precise sh ape of the signal and the detail of the noise pattern is unknown, In essenc e, we show how to determine the expected errors in the spectral parameters from an estimate of the SNR from a single spectrum, thereby allowing a more discriminative interpretation of the data. (C) 1998 Academic Press.