Basic tasks of signal processing in spectroscopy - Signal Processing in MRS with Biomedical Applications - page 11

turbative corrections are finally summed up, divergent results are invariably
obtained. This occurs because the coupling constant for strong interaction is
large and, as such, does not represent a good perturbation parameter for series
expansions. As a consequence, the perturbative solutions of renormalizable
field theories in strong interactions were severely limited to mainly under
standing certain analytical properties of the scattering S−matrix, without
yielding any quantitative predictions of observables [66]-[68]. Further, from
experimental measurements, a great many resonances were available awaiting
proper interpretations of mass spectra via quantitative predictions of positions
and widths of these unstable particle states. As such, the said perturbation
divergences made the entire theory of strong interactions unphysical but, here
again, the Pade approximant salvaged this situation by resumming divergent
series to the correct results. Moreover, experimental data on resonant scat
tering phenomena were and continue to be properly interpreted by the Pade
approximant which gave accurate predictions for positions and widths of peaks
in spectra for masses of metastable particles [69]-[72].
Overall, we emphasize that although the present book will primarily be
focused on spectral analysis of biomedical time signals from MRS in all the
concrete illustrations, the expounded general methodology remains applicable
as well to MRSI, and all other fields where FIDs can be described by linear
combinations of complex attenuated exponentials.

1.1 Challenges with quantification of time signals

At present, versatile MR modalities in medical diagnostics are widely consid
ered as one of the fastest expanding fields of the crossdisciplinary research
in medical physics. Nevertheless, the most recent vivid progress particularly
in MRS and MRSI, also uncovered the fact that the indispensable signal pro
cessing meets with huge challenges in reliably extracting information about
biochemical and physical functionality of the most clinically relevant metabo
lites of the investigated tissue. This type of information could be obtained
by MRS and MRSI under the assumption of achieving highquality, both in
encoding and signal processing. As to signal processing, it is mandatory to be
able to carry out unequivocal, accurate and robust quantifications of concen
tration of metabolites of the examined tissue. As mentioned, quantification
consists of spectral decomposition of the encoded FID into its harmonic con
stituents. Such a synthesis is achieved mathematically once the encoding
has been performed, because quantitative information cannot be extracted
directly from the encoded raw FID without resorting to signal processing.
In the framework of MRS, the signal processor which has been most fre
quently used is the FFT. The FFT is employed to e ciently convert the en