Signal Separation with A Priori Knowledge Using Sparse Representation - Advances in Heuristic Signal Processing and Applications - page 319

Fig. 14.3 Simulation of 1H human brain MRS spectra: ( a ) simulated resonances ( solid lines )and
simulated baseline ( dashed line ); ( b ) simulated observed spectrum with SNR = 30 dB and SBR =

10 dB

Here, for the consideration of computational efficiency, λ is set as Cε 2 , where ε
is the estimated noise power and C is a constant chosen by a thorough analysis of
simulated data.

14.3.4 Experiments and Results

In this section, this method is firstly used to process some simulated 1H human brain
MRS data and then its performance is compared with a commonly used nonlinear
parameter estimation method. Finally, some processing results of real clinical MRS
data are presented to illustrate the good performance of this method.

14.3.4.1 Simulated Experiments

(A) Simulated data
Each simulated 1H human brain MRS spectrum used here has 512 data points and
consists of 16 resonances, a baseline, and a Gaussian noise as shown in Fig. 14.3 .
The resonances are simulated as Gaussian functions, whose parameters are sum-
marized in Table 14.1 . The baseline is obtained from a similar baseline of a true
1H human brain MRS spectrum. Spectra are with different signal-to-noise ratios
(SNR

= =

5, 10, 15, and
20 dB). Here, SNR is defined as the ratio of the highest amplitude of these simulated
resonances to the noise standard deviation, and SBR is the power ratio of a mixed
spectrum of interest to the simulated baseline. For a given baseline and noise con-
dition, a set of 100 spectra is generated in order to give reliable estimation results

25, 30, 35, and 40 dB) and signal-to-baseline ratios (SBR