## 3 Results  
Figure 4a shows TARQUIN model fits and the baseline of the phantom data MR spectra while using a short TE PRESS sequence with a customized setting, where the reference signals are NAA, Creatine, Choline. In this customized setting, we only used the basis set of the existing metabolites of the phantom. The existing metabolites' basis set must be selected, because TARQUIN, by default, uses basis set of 26 metabolites and macromolecules to fit the MR spectra. Therefore, if the default setting is used for fitting the non-existing metabolites, it will cause over or under estimation of existing metabolites concentration and might report some metabolites concentrations that do not exist in the phantom. Even with this modified setting, TARQUIN may not e properly estimate the existing metabolite properly. For instance, as it is shown in the Figure 4, TARQUIN overestimates the baseline in two regions, where the peak of Glutathione and Glutamate is located. Thus, this overestimation leads to mis-quantification of these two metabolites. On the other hand, the creatine and NAA peaks are not detected properly and consequently did not match perfectly due to misalignment of their peaks with the basis sets. Therefore, NAA and Creatine are underestimated for the specific example that is provided in the Figure 4. \begin{table}
\begin{tabular}{c c} \hline \hline
**Metabolites** & **Concentration (mM/L)** \\ \hline NAA & 12.5 \\ Creatine & 10.0 \\ Choline & 3.0 \\ Myo-inositol & 7.5 \\ Lactate & 5.0 \\ GABA & 3.0 \\ Glutathione & 5.0 \\ Glutamate & 12.5 \\ Glutamine & 6.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Phantom data metabolites concentration. Figure 4b shows the fit of the proposed approach model to the phantom data and the estimated baseline. In the proposed approach, the estimated baseline is very smooth as compared to the TARQUIN estimation. In contract with TARQUIN, we model the baseline as a preprocessing step prior to model each metabolite MR spectra, while TARQUIN models the metabolite first and then considers the residual as the baseline. The subtraction of the baseline prior to modeling leads to more accurate estimation of the metabolite's MR spectra, as is shown in the Figure 4b. The main peaks including the NAA, Creatine, Choline, and Myo-inositol are matched more accurately with the MR spectra. More specifically, TARQUIN tries to detect the metabolites using basis sets matching, and then separates the baseline and the residue from the remaining part of the MR spectra, and, therefore, the detected metabolites overlap with the estimated baseline, and they are prone to over/under quantification. The metabolite concentrations of the phantom data in the five different regions are calculated and compared with TARQUIN; the average results along with their 95% confidence interval are provided, as shown in Table 3. The mean squared error (MSE) of each quantification method calculated using the provided ground truth of the phantom data in the Table 3. The proposed approach MSE is 0.34 while the MSE associated with the TARQUIN for the phantom data is 0.94. It is notable to mention that the proposed approach provides more accurate estimation of the six out of nine metabolites concentration. Figure 4: (**a**) The fitting phantom data magnetic resonance (MR) spectra using the TARQUIN; (**b**) The phantom data MR spectra fitted using the proposed approach. For both figures the phantom MR spectra (black), the fitted model (red), and the estimated baseline (green). Water signal was used as the internal reference to calculate brain metabolite concentrations [25; 38; 39]. Water intensities of all five different brain regions of one subject were compared to investigate the possibility of reducing the scanning time. The maximum and minimum water intensities were \(2.47\times 10^{9}\) and \(1.47\times 10^{7}\) in arbitrary unit, respectively.