Pad´e processing for MR spectra from in vivo time signals - Signal Processing in MRS with Biomedical Applications - page 250

7.5 Prospects for comprehensive applications of the fast
Pade transform to in vivo MR time signals encoded
from the human brain
In this chapter, we assessed the utility of the FPT for estimations of time sig
nals encoded by means of in vivo MRS. Convergence performance of the FPT
is demonstrated using two raw time signals encoded via MRS at the magnetic
field strengths of 4T and 7T from the brain of a healthy volunteer. All the
computed spectra are presented and analyzed in the absorption mode. The
employed signals of a su ciently long length (N = 2048) with the associated
bandwidth of 6001.5 Hz are of excellent SNR, so that the shape spectrum
from the FFT, using all N points, can give a reference spectrum.
The convergence rate of the FPT was monitored by gradually including
more and more signal points in the computations. It was observed that the
results of the FPT for one half and the full signal length were indistinguishable
from the background noise. Moreover, the convergence pattern of the spectra
predicted by the FPT was strikingly stable without spikes or any other spec
tral deformations. Further, the FPT yielded excellent estimates of the main
metabolites even for a quarter of the full signal length. This points to the
fast and accurate convergence of the FPT as a function of the signal length.
The residual or error spectra between the FPT (with either N/2 or N signal
points) and the FFT which utilizes the full FID are totally embedded in the
background noise.
The fidelity of the FPT was also crossvalidated internally using the two
equivalent variants, the FPT (+) and FPT (−) . Due to the uniqueness of the
FPT, all the physical resonances from the FPT (+) and FPT (−) must coincide
after convergence has been reached in both variants. Moreover, by employing
the full signal length N = 2048, the residual/error spectra for the difference
between the results from the FPT (+) and FPT (−) were found to be entirely
indistinguishable from background noise. Further, we computed the consecu
tive difference spectra as the difference between two consecutive values of the
partial signal lengths and found a remarkably fast convergence of the FPT (−) .
Overall, the FPT emerges as a powerful, stable processor with robust and
selfcontained error analysis for MR in vivo time signals. On top of providing
the shape spectra in any desired mode (absorption, dispersion, magnitude,
power), it should also be recalled that the FPT can simultaneously perform
quantification without fitting the FFT spectra or any other spectra. This
is clinically important for the needed accurate quantitative assessment of in
vivo time signals encoded via MRS from brain. A number of reasons are
highlighted for which the most recent advances in signal processing via the
paradigm shift initiated by the fast Pade transform could be of critical value
in early tumor diagnostics.