Exact quantum-mechanical, Pad´e-based recovery of spectral parameters - Signal Processing in MRS with Biomedical Applications - page 94

TABLE 3.1
Fourdigit accurate numerical values for all the input spectral parameters: the
real Re(ν k ) and imaginary Im(ν k ) parts of the complex frequencies ν k , and
the absolute values|d k |of the complex amplitudes d k of 25 damped complex
exponentials from the synthesized time signal (3.1) similar to a short echo time
(∼20 ms) encoded FID via MRS at the magnetic field strength B 0 = 1.5T
from a healthy human brain [88]. Every phase{φ k }of the amplitudes is set to

zero (0.000), i.e., each d k is chosen as purely real, d k =|d k |exp (iφ k ) =|d k |.

The letter M k denotes the k th metabolite.

INPUT DATA for ALL SPECTRAL PARAMETERS of a SYNTHESIZED TIME SIGNAL or FID

n o
k

Re( ν k ) (ppm) Im( ν k ) (ppm) |d k | (au) M k

1 0.985 0.180 0.122 Lip

2 1.112 0.257 0.161 Lip

3 1.548 0.172 0.135 Lip

4 1.689 0.118 0.034 Lip

5 1.959 0.062 0.056 Gaba

6 2.065 0.031 0.171 NAA

7 2.145 0.050 0.116 NAAG

8 2.261 0.062 0.092 Gaba

9 2.411 0.062 0.085 Glu

10 2.519 0.036 0.037 Gln

11 2.675 0.033 0.008 Asp

12 2.676 0.062 0.063 NAA

13 2.855 0.016 0.005 Asp

14 3.009 0.064 0.065 Cr

15 3.067 0.036 0.101 PCr

16 3.239 0.050 0.096 Cho

17 3.301 0.064 0.065 PCho

18 3.481 0.031 0.011 Tau

19 3.584 0.028 0.036 m−Ins

20 3.694 0.036 0.041 Glu

21 3.803 0.024 0.031 Gln

22 3.944 0.042 0.068 Cr

23 3.965 0.062 0.013 PCr

24 4.271 0.055 0.016 PCho

25 4.680 0.108 0.057 Water