Basic tasks of signal processing in spectroscopy - Signal Processing in MRS with Biomedical Applications - page 28

interpretable. The corresponding total shape spectrum is obtained by math
ematical transformation of the FID into its complementary representation in
the frequency domain. This total shape spectrum provides qualitative infor
mation, but not the quantitative one about the actual number of metabolites
that underlie each peak or the relative strength of individual components,
their abundance, etc. At best, the FFT takes us only to this second step.
More information is needed before the metabolites can be identified and their
concentrations reliably determined, and from the total shape spectrum alone
this can only be guessed (see section 3.1.4).
This undetected information can be extracted by novel and selfcontained
data analysis, namely the FPT, which we have introduced into MRS [5, 16]
with detailed implementations reported in Refs. [8]-[11] and [17]-[34]. In
this topic, we review the “proof of principle” evidence establishing that the
FPT meets the most stringent criteria imposed by clinical disciplines such
as oncology for MRS, as outlined in Refs. [10, 11] and [18]-[20]. The high
resolution and stability of the FPT have been clearly confirmed in our stud
ies of MR total shape spectra [8, 9], thereby overcoming one of the major
hindrances to wider application of MRS in clinical oncology. However, as
stated, total shape spectra do not provide the information needed to deter
mine how many metabolite resonances are actually present in the tissue and
in which concentrations. It is this information which is essential for improving
the diagnostic yield and accuracy of MRS in oncology. We demonstrate that
the FPT provides exact quantification of MR signals and thereby metabolite
concentrations are reliably and unequivocally obtained with an intrinsic and
robust error analysis [10, 11, 20, 34].
We have emphasized that there is an urgent need for accurate quantification
to determine metabolite concentrations, so that MRS can be better used to
detect and characterize cancers, with clear distinction from nonmalignant
processes. This is clearly illustrated by applying the FPT to time signals that
were generated according to in vitro MRS data as encoded from (a) malignant
and benign ovarian lesions [27, 29] as reviewed in chapter 9, (b) breast cancer,
fibroadenoma and normal breast tissue [32], as analyzed in chapter 10 and
(c) for cancerous prostate, normal stromal and glandular prostate [33], as
presented in chapter 11. We chose these problem areas because of their urgent
clinical importance.
This approach was made possible by widening the horizons of signal pro
cessing through finding its natural framework in a larger and wellestablished
theory - quantum physics [5]. By identifying the quantification problem in
signal processing as quantummechanical spectral analysis, the key door was
opened for using a highlydeveloped mathematical apparatus to overcome the
otherwise insurmountable di culties of the FFT, fittings and other similar
techniques [10, 11, 34]. It is through this direct connection of signal process
ing with quantum physics that a veritable paradigm shift has been established,
and the stage set for the emergence of the most powerful and versatile spectral
analyzer - the FPT.