Conclusion and outlooks - Signal Processing in MRS with Biomedical Applications - page 397

transfer, FFT. However, the ultimate goal is to extract the complete informa
tion from individual components as the constituent parts of these composite
spectral envelopes. This cannot be done by FFT. The present book suggests
that the optimal alternative method is the fast Pade transform, FPT, which
can provide both the qualitative (envelopes) and quantitative (metabolite con
centrations) information.
Thus, notwithstanding the need to broaden this mindset, what has mainly
prevented MRS and MRSI from realizing their potential in cancer diagnostics
and beyond, is the reliance upon total shape spectra without trustworthy
quantification. In other words, there is a vital need to reconstruct component
spectra and the spectral parameters from which metabolite concentrations are
computed. This requires a multidisciplinary approach. The key role here is
played by mathematics by which the measured time signals are transformed
into spectra. Spectroscopic methods are in fact the key strategy for studying
the structure and content of matter. The basic sciences, physics and chemistry,
developed their full potential using these methods. It is now time for medicine
to take advantage of such developments.
Clinical scanners used in MRI all rely upon the FFT. By inertia, this has
continued for MRS, even though the FFT lacks the necessary power to reveal
the true information content. The more appropriate spectroscopic methods
from physics and chemistry should have been transferred to MRS. Attempts
to compensate for the quantification inadequacy of the FFT in MRS have used
fitting, which is merely a form of patching which involves guesswork. The fun
damental issue here is not which fitting algorithm should be used, but rather,
that fitting is an inadequate, naive strategy for such a serious problem as
quantification in clinical diagnostics where underestimation via underfitting
(missing true metabolites) and overestimation through overfitting (“predic
tion” of false, nonexistent metabolites) are completely anathema. Fitting
can never unambiguously decipher the genuine, physical components hidden
under a given peak. This will invariably be uncertain and subjective in all
fitting techniques which are overwhelmingly in use in MRS and MRSI.
What are the alternatives? The first step is to properly define the task
of quantification in MRS. This amounts to the determination of metabolite
concentrations which are the norms, and then to find the potential correspon
dence between various patterns of deviation from normal and specific disease
processes. This is the role of clinical interpretation. The proper definition
of this task will be immensely facilitated by seeing the larger context. How
has spectral analysis, which is quantification, been achieved in neighboring
sciences? It is eminently clear that the key is mathematics, with rational re
sponse functions being the leading tool. Within these, the Pade approximant
is the method of choice because it uniquely solves the quantification prob
lem when the time signals are fully controlled. In the present book, we have
taken this road by developing the fast Pade transform. Through the FPT,
we tackled fully controlled problems with synthesized time signals that were
reminiscent of the related measured data.

We demonstrated that the FPT