Recapitulation of Pad´e-optimized processing of biomedical time signals - Signal Processing in MRS with Biomedical Applications - page 387

apeutic decisionmaking, in light of preliminary data [118] using changes in
total choline concentration to gauge the response to chemotherapy. One of the
main current problems with attempts at quantifying total choline has been
subjectivity due to the uncertainty with lower and upper integration limits
when using the procedure of numerical quadratures to determine the concen
tration via peak integration, as typically done [343, 443]. As mentioned, this
problem does not occur with the FPT, since this processor yields the spec
tral parameters uniquely, thereby obviating any subjective assessment about
where a given peak begins and ends.
Together with its stability and high resolution, these advantages indicate
that the fast Pade transform appears as the optimal processor for applications
of MRS and MRSI in clinical oncology. In summary, we enumerate the major
advantages of the FPT relative to other methods for processing MR spectra.
Specifically, the FPT:

•Uses only the originally encoded signal to extract the entire unique spec
tral information, in sharp contrast to the subjectivity of fitting recipes,
some of which require additional measurements merely to initialize the
leastsquare algorithms, only to end up with a biased preselection for
the very resonances that are sought,

•Provides e cient numerical algorithms and closed analytical formulae
for parametric and nonparametric signal processing (both can be used
simultaneously for crossvalidation),

•Truly embodies several powerful estimators with rigorous equivalence
to the autoregressive moving average, the Shanks transform, Pade
Lanczos approximant and continued fractions,

•Can e ciently compute the shape of a spectrum without prior extraction
of any of the spectral parameters{ω k ,d k },

•Greatly enhances resolution and signaltonoise ratio compared to the
FFT,

•Yields precise numerical data for all the peak parameters, i.e., the com
plex frequencies{ω k }and complex amplitudes{d k }that define the po

sition Re(ω k ), height |d k |, width Im(ω k ) and phase arg(d k ) for every

genuine (physical) resonance,

•Unequivocally extracts the exact number K of resonances directly from
the encoded time signal{c n }(0≤n≤N−1) by means of the two si

multaneous conditions for the Hankel determinants, in sharp contrast to
guessing done by other processors for which K is either underestimated
(missing genuine peaks) or overestimated (producing spurious peaks),

•Identifies with fidelity all the spurious (unphysical) resonances by nu
merical and analytical procedures via polezero cancellation (Froissart