Conclusion and outlooks - Signal Processing in MRS with Biomedical Applications - page 395

can be used in the whole field of signal processing as the most reliable method
to date for disentangling genuine from spurious information. In system theory
as well as in control theory from engineering, stability of the system's param
eters is the prerequisite for the system's overall performance. Both zeros and
poles of response functions play their crucial roles in the sought stability of
systems. Not unexpectedly, the Pade approximant has been firmly established
over the years as the optimal response function in both system and control
theory. This fully coheres with the like experience from quantum physics as
emphasized throughout this topic and mentioned in the outlined example (i)
and (ii). Moreover, Froissart doublets are the proof that zeros of the Pade
response function are critical to finding stability of the examined system. Gen
uine zeros remain in the final output of the performed data analysis as stable
structures of the studied system, while spurious ones as unstable Froissart
zeros are washed out by being canceled by the corresponding spurious poles
at the coincident positions in the complexvalued frequency spectra.
Equipped with the exact quantification and accompanied by signalnoise
separation via identification as well as through subsequent discarding of Frois
sart doublets leading de facto to noise suppression, the Pade approximant
emerges as the theory of choice for spectral analysis of quantification of gen
eral time signals. Our implementations of such pivotal developments within
magnetic resonance spectroscopy give a fresh and new platform to the other
wise unprecedentedly rich theory and practice of Pade approximants as they
apply to life sciences in general, and clinical diagnostics, in particular.

13.2 Outlooks for Pade-optimized MRS and MRSI from

a clinical perspective

Diagnostics obviously play a central role in medical practice, particularly in
oncology. Clinical decisionmaking vitally depends upon the knowledge of
whether or not a malignancy is present, and if so, its nature and extent. This
information is crucial for guiding therapy as well as for subsequent surveil
lance. Early cancer detection holds the promise of improved prognosis and the
need for less radical treatment. This is the motivation for screening programs
aimed at malignancies of major public health importance such as breast and
prostate cancer. These programs have succeeded in increasing survival. Ovar
ian cancer remains a major cause of death among women precisely because
of the lack of early detection. Primary brain tumors are less common than
the other three mentioned malignancies. Nevertheless, they draw a great deal
of attention, often have poor prognosis and it is here that the most delicate
of clinical decisions are made, requiring maximal information of the highest
possible reliability. These four types of cancers are those upon which we have
focused in this topic on spectral analyses of the pertinent data.