Exact quantum-mechanical, Pad´e-based recovery of spectral parameters - Signal Processing in MRS with Biomedical Applications - page 148

rameters even for rather small uncertainties in the encoded time signal. These
uncertainties can arise from a number of sources, including experimental er
rors, statistical effects manifested as noise, etc. In addition, the methods of
spectral analysis can contribute to further uncertainties via computational
roundoff errors, algorithmic instabilities, etc. In attempting to deal with all
these types of corruption of the analyzed data, one typically confronts major
obstacles. This is certainly the case also for newly designed methods such as
the FPT which is herein applied to the specific area of MRS.
The prudent approach to such a challenging problem would, therefore, be
to systematically evaluate the validity and the overall performance of a given
processor using realistically synthesized time signals. These would be noise
free as well as noisecorrupted. Such a systematic strategy is necessary to
gain confidence while establishing the validity of the selected estimator when
the solution of the quantification problem is known. This gives a much better
chance for reliability of estimations for FIDs that are measured experimentally.
For the theoreticallygenerated time signals, the fundamental frequencies and
amplitudes are known from the onset. Thereby, the evaluation can be focused
upon testing the accuracy, robustness and reliability of the estimator. Syn
thesized noiseless FIDs merit special investigation as done herein, since every
step in the analysis is completely controllable, starting with the input data
until all the information is reconstructed. Thus, we hereby demonstrate that
the FPT exhibits an unprecedentedly high performance for each critical step
in the exact solution of the quantification problem in MRS.
From the highresolution spectral analysis presented herein for noiseless
synthesized FIDs, and considering the results obtained together with their
importance for furthering the field of MRS, in particular for applications to
clinical oncology, the following central question is asked. Is it realistic to utilize
the remarkable reliability of the FPT, according to all the predictions of the
quantummechanical spectral analysis and signal processing, to carry out the
most accurate and robust quantification also for noisecorrupted synthesized
as well as encoded in vivo MRS time signals? The answer in the a rmative
to this key question can be surmised from our investigations on the level of
estimation of envelope spectra computed by the FPT using FIDs encoded by
in vivo MRS [8, 9]. Although in these investigations, quantification problems
have explicitly been solved by the FPT prior to construction of such spectra,
the concrete detailed information was not reported, especially about the sensi
tivity of all the reconstructed fundamental frequencies and amplitudes to the
presence of noise in the encoded FIDs. This should be done in a systematic
manner for both synthesized noisecorrupted and encoded FIDs. We have, in
fact, performed this demanding task in chapter 6 by extending strictly the
Pade methodology to noisepolluted FIDs. As a preview, we stress that the
role of Froissart doublets or polezero cancellation for distinguishing physical
from nonphysical harmonics, as demonstrated herein for noiseless FIDs, is
of key importance for identifying the genuine resonances in noisecorrupted
FIDs and clearly differentiating them from spurious content.