Multiplet resonances in MRS data from normal and cancerous prostate - Signal Processing in MRS with Biomedical Applications - page 368

tiplets and closely overlying resonances of different metabolites for all three
problems under study here, namely for normal glandular and normal stromal
prostate, as well as for the spectra from prostate cancer.
For the normal glandular prostate data convergence was attained at N P =
700 and for the normal stromal and the malignant data at N P = 600 for the
given total signal length N = 1024. At those partial signal lengths, the FPT
exactly reconstructed all the spectral parameters for the time signals corre
sponding to the normal glandular and stromal prostate, and to the prostate
cancer.
Since 2K = N P , at these convergence lengths N P there were 350, 300 and
300 resonances, respectively for the normal glandular prostate, normal stromal
tissue and for the malignant case. Of these, only twentyseven were genuine,
the other 323 and 273, respectively were spurious, and were identified as such
by zero amplitudes and the polezero coincidences. Thus, there were over
eleven times and over ten times more spurious resonances than those that
were genuine, respectively.
The number of spurious resonances (and their percentage in relation to
those that are genuine) for the present prostate cancer MRS problem was much
larger than for the ovarian cancer problem described to which we applied the
FPT [27, 29], but fewer than for the breast cancer problem [32], as presented
in the preceding chapters.
This is a reflection of some of the more subtle aspects of spectral processing,
notably the smallest distance among the poles and zeros, the density of poles
and zeros in the complex plane, as well as interseparations among poles and
zeros [34].
For the problems addressed in this chapter, it would be theoretically pos
sible to retrieve all twentyseven input resonances at N P = 54 because there
are 54 unknowns (27 complex frequencies and 27 complex amplitudes) with
54 linear equations and 54 signal points needed.
At N P = 54 twentyseven resonances were indeed retrieved, but fifteen
of these resonances were spurious for the normal glandular case and sixteen
were spurious for the normal stromal and prostate cancer cases. The pole
zero coincidences of the FPT (yielding zerovalued amplitudes) allowed us to
identify these spurious resonances, and to thereby determine that only the
remaining twelve or eleven were genuine.
Convergence seems to commence at the outermost spectral regions, with
lactate and alanine at about 1.33 ppm and 1.49 ppm, respectively and with
myoinositol and lactate at about 4.07 ppm and 4.12 ppm, respectively. The
inner, denser spectral region converged later.
The last resonances to converge were those closest to the real axis with the
smallest imaginary part of ν − k . It should be pointed out that at a very few
signal points prior to convergence, there could still be an admixture of the
absorption and dispersive modes, since the latter appear intermittently.
At convergence and beyond, the dispersive mode completely disappeared,
so that the absorption spectrum was purely in the absorption mode, i.e., the