Pad´e quantification of malignant and benign ovarian MRS data - Signal Processing in MRS with Biomedical Applications - page 288

CONVERGENCE of PADE and FOURIER ABSORPTION TOTAL SHAPE SPECTRA for VARYING FID LENGTH (BENIGN)
FAST PADE TRANSFORM, FPT (−) : TOP PANELS (i) & (ii) , FAST FOURIER TRANSFORM , FFT : MIDDLE & BOTTOM PANELS (iii) − (vi)

Pade Absorption Total Shape Spectrum Pade Absorption Total Shape Spectrum

4000 4000

B 0 ≈ 14.1T

N/32 = 32 (N = 1024)
FPT (−)

B 0 14.1T

N/16 = 64 (N = 1024)
FPT (−)

≈

Benign Benign

Lac

2000 2000 Lac

Glc Glc

1000 1000

500 500

300 300

Converged Ala

Gln Gln

200 200

100 100 Lys Val

Val Thr

Crn

50 50

Ala Cr

30 30

Cr

Crn

20 20

Lys

10 10

Cho

Iso

Met

5 5

3 3

2 2

1

Met

1

0.5 0.5

5 4 3 2 1.5 1 5 4 3 2 1.5 1

(i) Chemical shift (ppm) (ii) Chemical shift (ppm)

Fourier Absorption Total Shape Spectrum Fourier Absorption Total Shape Spectrum

10 50

B 0 ≈ 14.1T

N/32 = 32 (N = 1024)
FFT

B 0 14.1T

N/16 = 64 (N = 1024)
FFT

≈

Benign Benign

7.5 40

5 30

2.5 20

0 10

−2.5 0

−5 −10

5 4 3 2 1.5 1 5 4 3 2 1.5 1

(iii) Chemical shift (ppm) (iv) Chemical shift (ppm)

Fourier Absorption Total Shape Spectrum Fourier Absorption Total Shape Spectrum

4000 4000

B 0 ≈ 14.1T

N = 8192
FFT

B 0 14.1T

N = 32768
FFT

≈

Benign Benign

2000 2000

1000 1000

500 500

Converged 300 300

200 200

100 100

50 50

30 30

20 20

10 10

5 5

3 3

2 2

1 1

0.5 0.5

5 4 3 2 1.5 1 5 4 3 2 1.5 1

(v) Chemical shift (ppm) (vi) Chemical shift (ppm)

FIGURE 9.2
Absorption total shape spectra for the benign ovarian case using input data
derived from Ref. [343]. Pade and Fourier convergence rates: the top panels
(i) [N/32 = 32] and (ii) [N/16 = 64] correspond to the FPT, whereas the
FFT is on the middle (iii) [N/32 = 32] and (iv) [N/16 = 64], as well as on
the bottom panels (v) [N = 8192] and (vi) [N = 32768].