Converged absorption total shape spectra

Figure 6.20 Converged absorption component shape spectra (top panel (i)) and converged absorption total shape spectra (bottom panel (ii)) both reconstructed by the FPT based on in vitro MRS data from Ref. [54] for normal glandular prostate.

We present the absorption component shape spectra and the total shape spectra as reconstructed by the FPT for the normal breast data in Figure 6.10 at three partial signal lengths Np = 1000,1500, and 2000. The top right panel (iv) indicates that at Np = 1000, the absorption total shape spectrum has converged. In contrast, for the component shape spectrum (top left panel (i)), there is only one peak (phosphoethanolamine. A = 5) at 3.22 ppm that has been overestimated, whereas phosphocholine, (A = 4) has not been detected. 

The converged absorption component shape spectrum (top panel (i)) and total absorption shape spectrum (lower panel (ii)) for prosfafe cancer between 2.40 and 3.70 ppm at Np = 800 are compared in Figure 6.26. Strikingly, the serrated peaks on the total shape spectrum only suggest the number of underlying resonances. The converged componenf specfrum is essential to visualize the actual number and structure of resonances. For example, from the small polyamine peaks, it would be difficult to know that there are actually two components. 

Figure 4.8 Absorption component shape spectra (left) and absorption total shape spectra (right) from the FPTf 1 near full convergence for signal lengths Np = 180,220,260. On panel (iv) for Np = 180, the total shape spectrum reached full convergence, despite the fact that on panel (i) for the corresponding component shape spectra, the 11th peak is missing and the 12th peak is overestimated.

Figure 6.25 Absorption total shape spectra reconstructed by the FPT for MRS prostate cancer data as encoded in vitro in Ref. [54]. The upper panel (i) is at Np = 54 and the converged spectrum at Np = 800 is shown on the lower panel (ii).

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