Pad´e processing for MR spectra from in vivo time signals - Signal Processing in MRS with Biomedical Applications - page 240

At N/8 = 256 shown on the left bottom panels of Figs. 7.4 and 7.8 , the
concentration of NAA predicted by the FPT (−) achieves nearly 100% of the
correct NAA concentration. Moreover, at this oneeighth signal length, the
FPT (−) yields nearly 90% of the true concentrations of the other two main
metabolites that are creatine and choline, at approximately 3.0 ppm and 3.3
ppm, respectively.
A very important finding from Figs. 7.4 and 7.8 (left bottom panels) is that
at 4T and 7T, respectively, already at N/8 = 256, the FPT (−) predicts the
nearly correct peak height ratio of creatine and choline. With the FFT, the
correct peak height ratio of creatine and choline at, e.g., 4T is not obtained
even at N/2 = 1024 (middle right panel in Fig. 7.3 ) .
The upper right panels of Figs. 7.4 and 7.8 show the Pade absorption
spectrum at N/4 = 512. At a quarter of the FID at 4T, the FPT (−) is able
to reconstruct practically all the major metabolites with the exception of
the triplet glutamineglutamate (near 2.4 ppm) which appears as a single,
unresolved peak. On the middle right panel in Figs. 7.4 and 7.8, the spectrum
computed by the FPT (−) is depicted at N/2 = 1024. Here, at one half of the
FID, it is seen that the FPT (−) clearly resolves the remaining glutamine

glutamate triplet.
Furthermore, up to differences on the level of the background noise, the
FPT (−) gives practically the same spectra at N/2 and N (middle and bottom
right panels of 7.4 and 7.8). This means that the total shape spectra in the
FPT (−) has fully converged at N/2, so that the second half of the examined
FID might not be indispensable. By comparison with Figs. 7.3 and 7.7
(middle and bottom right panels), the FFT needs to exhaust the full FIDs
(N = 2048) to completely resolve the glutamineglutamate triplet near 2.4
ppm at both field strengths, 4T and 7T.
A direct comparison between the FFT and the FPT (−) carried out via the
same graphs, as done on Figs. 7.5 and 7.6 at 4T as well as in Figs. 7.9 and
7.10 at 7T shows that the latter converges faster than the former. Moreover,
it is clear from this juxtaposition that resolution is much better in the FPT (−)
than in the FFT at any truncation M > 1.
Remarkably, at N/32 = 64, the overall shape of the spectrum in the FPT (−)
has already emerged, whereas the corresponding FFT displays only broad
bumps near some of the true resonances (the top left panels in Figs. 7.5
and 7.9). On the middle right panels in Figs. 7.5 and 7.9 (N/16 = 128),
the FPT (−) is seen to be able to clearly resolve several among the major
resonances such as NAA. In sharp contrast, it is seen in Fig. 7.5 that at 4T,
the FFT does not even exhibit the presence of NAA at these two partial signal
lengths. On the bottom right panels in Figs. 7.5 and 7.9 (N/8 = 256), the
FPT (−) has further improved its prediction of the concentration of NAA at
≈2.02 ppm, Cre at≈3.0 ppm and Cho at≈3.3 ppm. On the other hand,
at N/8 the FFT continues to greatly underestimate the concentrations of all
the metabolites, and the resulting Fourier spectrum is still seen to be very