Absorption total shape spectra

Figure 4.2 Time signal (panels (i), (ii)) and the corresponding absorption total shape spectra (envelope) in the FPT (panels (iv), (v)) and FFT (panel (vi)). The initial convergence regions in the FPT(+) and FPT, ), inside and outside the unit circle, respectively, are shown on panel (iii).

CONVERGENCE of ABSORPTION TOTAL SHAPE SPECTRA (FFT Left, FPT Right) FID LENGTH N/M, N = 1024, M = 1-8... 

Figure 4.3 Convergence rate as a function of the partial signal length Np at the fixed band-width, 1000 Hz. Fourier (FFT, left panel) and Pade (FPT right panel) absorption total shape spectra computed using the time signal from Figure 4.2 at different partial signal lengths, as well as at the whole FID (N = 1024).

Figure 4.4 Fourier (FFT, left column) and Pad (FPT(, right column) absorption total shape spectra computed using the time signal (divided by TO4) at the partial signal lengths N/16 = 128, N/4 = 512, and N/2 = 1024 on the top, middle, and bottom panels, respectively, where the full signal length is N = 2048, as experimentally measured in Ref. [72] at 4T from brain occipital gray matter of a healthy volunteer.

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 6.1 Absorption total shape spectra for the benign ovarian cyst fluid from input data derived from Ref. [23]. The signal lengths are N/32 = 32 (top panels (i), (iv)), N/16 = 64 (middle panels (ii), (v)), and N/8 = 128 (bottom panels (iii), (vi)), where N is the full signal length (N = 1024). Spectra generated by the FFT are shown on the left panels and by the FPT on the right panels.

CONVERGENCE of FADE and FOURIER ABSORPTION TOTAL SHAPE SPECTRA for VARYING FID LENGTH (BENIGN)... 

Figure 6.5 Absorption total shape spectra generated by the FFT for the benign and malignant ovarian cyst fluid using input data derived from Ref. [23]. The signal lengths are N = 8192 (upper panels), N = 16384 (middle panels) and N = 32768 (lower panels, where the spectra converge). The benign and malignant cases are shown respectively on the left and right columns.

Figure 6.19 Absorption total shape spectra for normal glandular prostate reconstructed by the FPT based on in vitro MRS data from Ref. [54]. The top panel (i) is at Np = 54, and the converged spectrum at Np = 800 is shown on the bottom panel (ii).

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