Exact quantum-mechanical, Pad´e-based recovery of spectral parameters - Signal Processing in MRS with Biomedical Applications - page 103

induction decay curve is heavily packed with exponentially decaying oscilla
tions and no other discernable structure appear. Specifically, it is impossible
to decipher any clinically meaningful information by inspecting an FID di
rectly in the measured time domain. However, from such a time signal one
can compute an MR spectrum which exhibits the definite advantage of dis
playing a relatively small number of distinct characteristics that are amenable
to further analyses and interpretations for clinical purposes. A typical total
shape spectrum of this type is shown in the middle panel (ii) in Fig. 3.2 in
the absorption mode.
This is obtained by a simple and powerful mathematical transformation
of the original time signal into its dual or complementary representation in
the frequency domain. The advantage of this passage to the frequency rep
resentation is manifested in the emergence of a number of clearly discernable
features through the appearance of peaks and valleys. Nevertheless, the to
tal shape spectrum is merely an envelope which, at best, could provide only
qualitative information about the overall contribution from the sum of all the
constituent resonances, but not the individual components themselves that
are seen on panel (iii) in Fig. 3.2, as reconstructed by the FPT (−) . Thus,
despite being more revealing than the time signal, the spectral envelope from
panel (ii) is still only qualitative as well as inconclusive and, as such, often of
limited clinical usefulness. Yet, the FFT, as the most frequently used signal
processor in many interdisciplinary applications, including MRS, is restricted
to computations of total shape spectra alone.
Overall, the absorption total shape spectra cannot directly provide the in
formation about any feature of resonances, such as the clinically most impor
tant concentrations of the underlying metabolites of the scanned tissue. In
direct information is often guessed from these spectral Fouriertype envelopes
by attempting to fit a subjectively preassigned number of resonances hidden
beneath each peak structure. These fittings constitute the usual technique
encountered in the MRS literature, despite the obvious drawbacks of such a
naive approach to spectral analysis. The most serious of these drawbacks is
nonuniqueness, which stems from the fact that virtually any chosen number
of components could equally well produce an acceptable error in the con
ventional leastsquare adjustments to the given spectral envelope. Hence, it
would be far more clinically advantageous to have an alternative mathematical
transformation, which would use only the original, unedited, raw time signal
to first obtain the unique spectral parameters of each peak (position, width,
height, phase) and then, if desired, to generate the component as well as total
shape spectra in any of the selected modes (absorption, dispersion, magni
tude, power). Nevertheless, such spectra with curves, although convenient,
are only for visual inspection.
Most important are the numerical values of the retrieved spectral param
eters and especially metabolite concentrations. The reason being that, when
analyzing clinically encoded FIDs, it is only with these numbers from ta
bles (rather than with envelopes from graphs) that the adequate quantita