Biomedical Engineering Reference
In-Depth Information
a
d
3
3
PADE: FPT
(−)
FOURIER: FFT
B
0
=4T
B
0
=4T
2.5
2.5
N/32 = 64
N/32 = 64
2
2
1.5
1.5
1
1
0.5
0.5
0
0
5
4
3
2
1
5
4
3
2
1
Chemical shift (ppm)
Chemical shift (ppm)
b
e
3
3
PADE: FPT
(−)
FOURIER: FFT
B
0
=4T
B
0
=4T
2.5
2.5
N/16 = 128
N/16 = 128
2
2
1.5
1.5
1
1
0.5
0.5
0
0
5
4
3
2
1
5
4
3
2
1
Chemical shift (ppm)
Chemical shift (ppm)
c
f
3
3
PADE: FPT
(−)
FOURIER: FFT
B
0
=4T
B
0
=4T
2.5
2.5
N/2 = 1024
Not Converged
N/2 = 1024
Converged
2
2
1.5
1.5
1
1
0.5
0.5
0
0
5
4
3
2
1
5
4
3
2
1
Chemical shift (ppm)
Chemical shift (ppm)
Fig. 25.3
Fourier and Pade absorption spectra computed using the time signal (divided by 10000)
at three partial signal lengths
.N=32 D 64; N=16 D 128; N=2 D 1024/;
where the full signal
length is
N D 2048;
as encoded in [
18
] at 4T from occipital grey matter of a healthy volunteer
of normal prostate tissue and malignant prostate. Pade-based reconstruction yielded
the exact spectral frequencies and amplitudes of all the resonances and provided
certainty about their true number. The “spectral crowding” problem does not hinder
the FPT, which via parametric analysis, without fitting or numerical integration of
