Basic tasks of signal processing in spectroscopy - Signal Processing in MRS with Biomedical Applications - page 27

cost, higher field MR scanners with stronger static magnetic fields obviously
provide better SNR, thereby yielding improved spectral quality.
Notwithstanding the importance of these technical, i.e., hardware consider
ations, and the need for further advances in this area, the critical limitation
of current applications of MRS and MRSI is directly related to reliance upon
the conventional signal processing method, the fast Fourier transform and the
accompanying post processing via fitting and/or peak integrations. The more
advanced mathematical methods that are the focus of this topic are the vital
remedy. The strategic importance of robust and uniform data processing of
MRS signals has been strongly emphasized [107, 119] at, e.g., the expert meet
ing on MRS for oncology, held recently by the U.S. National Cancer Institute
[107], as well as at a special conference in November 2006 on Data Processing
in MR Spectroscopy and Imaging by the International Society for Magnetic
Resonance in Medicine.
One may wonder: how could mathematics play such a critical role in medi
cal diagnostics? This is because data encoded directly from patients by means
of existing imaging techniques, e.g., computerized tomography (CT), positron
emission tomography (PET), single photon emission tomography (SPECT),
ultrasound (US), as well as MRI [12, 120] and MRS [5, 8] are not at all
amenable to direct interpretation, which therefore need mathematics via sig
nal processing.
The starting point for grasping the basics of signal processing in medical di
agnostics is the concept of “conjugate variables”. Unfortunately, this concept
is rarely explained in an intellectually satisfying manner for those whose pri
mary expertize is distant from the realm of mathematics and physics. Rather,
far too prematurely, technical terminology is usually introduced, and this is
done with inadequate definition. The result is often hazy thinking about such
important relationships as that between kspace (momentum space) and the
image obtained from the MR scanner. We would like to emphasize the tremen
dous intellectual gratification when we grasp that this relationship is closely
analogous to that between time signals and their spectral representation.
Biomedical researchers and clinicians should readily appreciate that diag
nostically important information can sometimes be di cult to quantify, and
may not even be apparent in the domain in which it is recorded. Familiar il
lustrations include slow activity on the electroencephalogram, 60120 Hz late
potentials and heart rate variability in the 0.15 to 0.4 Hz range on the elec
trocardiogram, to name a few. The reason for which spectral analysis of these
physiological signals is justified is that time and frequency are complemen
tary representations or conjugate variables. We also proceed to another set of
conjugate variables, momentum and position, from whence the k space rep
resentation is transformed into an MR image in the more familiar coordinate
spatial representation. The next logical step is to examine the mathematical
procedures needed to achieve this transformation.
In MRS, the encoded data are heavily packed time signals that decay expo
nentially in an oscillatory manner. These time domain data are not directly