Pad´e quantification of malignant and benign ovarian MRS data - Signal Processing in MRS with Biomedical Applications - page 293

illustrate the rapid convergence of the FPT achieved at N/16 = 64 signal
points (right upper panel). At signal lengths N/32 = 32 and N/16 = 64
the FFT is also rough and uninformative for the malignant cyst data (middle
panels in Fig. 9.4 ) . The bottom panel in Fig. 9.4 shows the convergence
pattern of the absorption spectra in the FFT at the two large signal lengths
(N = 8K = 8192,N = 32K = 32768). The first FID length for which the
positivedefinite Fourier absorption spectra are obtained is at (N = 8K). All
the twelve resonances are resolved in the FFT at N = 8K on the lower left
panel in Fig. 9.4. However, several peak heights are incorrect. At N = 8K
there are once again significant baseline distortions which, as noted, would
invalidate both fitting and numerical peak integrations. The FFT converges
at N = 32K = 32768, as shown on the lower right panel in Fig. 9.4 for the
malignant case.
9.3.3 Summary comparisons of the performance of FPT and
FFT for MRS data derived from benign and malignant
ovarian cyst fluid
Table 9.4 provides a summary of the convergence performance of the FPT for
the MRS data derived from benign (left panel) and malignant (right panel)
ovarian cyst fluid at the partial signal lengths N/32 = 32,N/16 = 64 and
N/8 = 128. The computed concentrations for both the benign and malignant
cases are fully correct at N/16 = 64 (middle panels), since the spectral pa
rameters for all twelve metabolites are exact to six decimal places. Stability
of convergence is shown on the bottom panels at N/8 = 128.
Figure 9.5 shows the performance of the FFT for the absorption total shape
spectra, at three much longer signal lengths: N = 8K = 8192 (top panels),
N = 16K = 16384 (middle panels) and N = 32K = 32768 (bottom panels).
The performance of the FFT for the benign ovarian cyst data is presented on
the left column and for the malignant ovarian cyst data on the right column.
As noted, at N = 8K = 8192 all the twelve resonances are resolved, but not
all their peak heights are correct for the benign nor for the malignant ovarian
case. At N = 16K = 16384 the peak heights are still not correct for either
case. It is only at N = 32K = 32768 signal points that all the peaks have
reached their correct heights for the benign and malignant ovarian cyst data,
since convergence has been achieved by the FFT. This figure illustrates the
importance of determining the point of convergence, since prior to that point,
baseline distortions as well as incorrect peak heights would render all attempts
at assessing metabolite concentrations completely tenuous.
The convergence patterns of the reconstructed absorption total shape spec
tra via the FPT are recapitulated for the benign (left column) and malignant
(right column) cases in Fig. 9.6 . The three signal lengths are N/32 = 32 (top
panels), N/16 = 64 (middle panels) and N/8 = 128 (bottom panels), with
convergence attained for both cases at N/16 = 64.
Figure 9.7 provides a summary comparison between the signal length at