Pad´e quantification of malignant and benign ovarian MRS data - Signal Processing in MRS with Biomedical Applications - page 292

CONVERGENCE of PADE and FOURIER ABSORPTION TOTAL SHAPE SPECTRA for VARYING FID LENGTH (MALIGNANT)
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 (−)

≈ Lac

Malignant Malignant

2000

Lac

2000

1000 1000

Gln Gln

500 500

Ala

Lys

300 300

Converged

Val

Val

Thr

200

Glc

200

Glc

100 100 Lys

Crn Iso

Ala Met

50 50

Cr

30 30

Cho

20

Crn

20

Cr

10 10

5 5

Met

3 3

2 2

1 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

120

B 0 14.1T

N/16 = 64 (N = 1024)
FFT

≈

B 0 ≈ 14.1T
N/32 = 32 (N = 1024)
FFT

Malignant

20

Malignant

100

15

80

10

60

5

40

0

20

−5

0

−10 −20

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

≈

Malignant Malignant

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

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

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

FIGURE 9.4
Absorption total shape spectra for the malignant 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
bottom panels (v) [N = 8192] and (vi) [N = 32768].