Multiplet resonances in MRS data from normal and cancerous prostate - Signal Processing in MRS with Biomedical Applications - page 346

While the correct value was 0.468435 au, the reconstructed |d − k

ww. | was

1.066128 au for GPC at N P = 600.
Full convergence was achieved at N P = 700 for all the reconstructed pa
rameters and computed concentrations for each of the 27 resonances (bottom
panel (ii) of Table 11.4 ) . The stability of convergence was verified at higher
partial signal lengths as well as at the total signal length N = 1024.
In Fig. 11.1 the absorption component shape spectra as reconstructed by
the FPT (−) are shown at the two partial signal lengths: N P = 54 and N P =
800 for the normal glandular prostate data. At N P = 54, fifteen of the twenty
seven resonances were missing (top panel). It was only at the two extremes
of the spectrum that all the resonances were resolved and that heights were
close to being correct (lactate and alanine at 1.33 ppm and 1.49 ppm and
myoinositol and lactate at about 4.07 ppm and 4.12 ppm, respectively).
For the denser spectral region from≈2.5 ppm to 3.70 ppm, only eight
of the twentythree peaks were resolved and an admixture of the absorption
and dispersive modes are seen, the latter includes structures with negative
intensities on the ordinate axis. The relative heights of the doublet citrate
peak near 2.5 ppm are seen to be reversed, namely the peak at about 2.52 ppm
is larger than the one at about 2.54 ppm. The second citrate peak near 2.75
ppm is seen to be a singlet, although it should be a doublet. The peaks near
3.55 ppm and 3.65 ppm corresponding to myoinositol also appear as singlets,
when they should be triplets. Three broad peaks at≈3.05 ppm, 3.22 ppm
and 3.3 ppm are seen, but there should be ten peaks within that spectral
region. These three broad peaks all have dispersive features with negative
intensities. The lower panel of Fig. 11.1 at N P = 800 shows that all 27
resonances were resolved with correct peak heights including all the multiplet
resonances and the overlapping resonances of phosphocholine at 3.23 ppm and
glycerophosphocholine at 3.24 ppm. The dispersive modes have disappeared
at N P = 800.
Herein, the case with N P = 54 is shown since this is the least number of
signal points which is theoretically needed to resolve 27 resonances (27 un
known frequencies and 27 unknown amplitudes considered in concert require
54 linear equations). However, it is seen from panel (i) of Fig. 11.1 that this
algebraic condition of completeness (N P = 2K = 2×27) is totally insu cient,
primarily due to the high density of states. Thus, not 2K but more than 10K
signal points are needed for densely packed spectra such as these.
Figure 11.2 shows the total absorption shape spectra reconstructed by the
FPT (−) at the same two partial signal lengths N P = 54 (top panel (i)) and
N P = 800 (bottom panel (ii)) for the normal glandular prostate data. As was
the case for the component shape spectra at N P = 54, the relative heights of
the doublet citrate peak near 2.5 ppm are reversed, i.e., the peak at around
2.52 ppm is larger than the one at 2.54 ppm, and the second citrate peak
near 2.75 ppm appears as a singlet, when it should be a doublet. The peaks
near 3.55 ppm and 3.65 ppm corresponding to myoinositol, appear as singlets,
although they should be triply serrated. It was just for those resonances in the