Magnetic resonance in neuro-oncology: Achievements and challenges - Signal Processing in MRS with Biomedical Applications - page 264

of various metabolites differ, not only peak heights, but also peak ratios can be
affected by changes in TE [252, 259]. Thereby, reliance upon metabolite ratios
also becomes more problematic. Thus, for example, Kaminogo et al. [252]
report that the NAA to choline ratios assessed from MR spectra obtained at
short TE were of limited value in brain tumor grading. These authors [252]
note that besides NAA, “the peak around 2.0 ppm may contain other fractions
of metabolites, including lipids at 2.05 ppm, and glutamate and glutamine at
2.1 ppm and 2.5 ppm ... Especially at short TE spectroscopy, Glx and lipids
may contribute to the spectral area at 2.0 ppm and possibly affect grading”
(p. 361). The problem of assessing NAA levels at short TE is thus related to
the presence of overlapping resonances that cannot be identified unequivocally
by Fourier processing and postprocessing fitting.

8.2.1.3 Advantages for brain tumor diagnostics by the high reso-

lution of the fast Pade transform

As discussed, one of the key advantages of the fast Pade transform relative to
the FFT is that convergence is not only stable, but also rapid. This means
that even at short signal lengths, the FPT is still capable of determining the
true concentrations of the main metabolites that remain undetected by the
FFT. A spectrum in the FPT does not use the fixed Fourier mesh in the fre
quency domain, and can be computed at any frequency. Thus, resolution is
not predetermined by the total acquisition time T. The conundrum between
increasing acquisition time for improved resolution and increasing noise is
thereby obviated by the FPT. This is especially important for accurate detec
tion of shortlived metabolites. In brain tumor diagnostics, we have seen that
a number of informative metabolites, notably, lipids, glutamine - glutamate,
and myoinositol decay rapidly and, therefore, require shorter echo times in
order to be adequately detected.
We have also reviewed another very important advantage of the FPT,
namely, its power of extrapolation. The FFT is limited by a sharp cutoff
of the time signal at the end of the acquisition time T, replacing any exten
sion of the signal by zeros or using the signal periodic extension, with no new
information in either case. However, the FPT uses its polynomial quotient
to extrapolate beyond the given T, and this is the main contributor to the
markedly improved resolution [18]. As noted, the FFT has a poor SNR in
part due to the need for long acquisition times. The poor SNR of the FFT is
also related to the fact that it is a linear mapping where the transformation
coe cients are independent of the time signal points. The FPT is a nonlinear
mapping, such that its coe cients are dependent upon the time signal points.
Thus, while the linearity of the FFT preserves noise from the time signal, the
nonlinearity of the FPT permits noise suppression. Numerical computations
from Ref. [35] show that the FPT is powerful for noise suppression especially
in the vicinity of genuine signal poles. Furthermore, the FFT has a linear
convergence (1/N) with increased signal length N, whereas the convergence