## 4 Discussion  
In this paper, a new data-driven algorithm for MRS signal analysis is proposed, which decomposes the FID signal in the time domain and clusters the decomposed components in the frequency domain while using prior knowledge of the chemical structure of different metabolites within the selected voxel. Although the algorithm is generalized, we have focused on the analyzing short TE \({}^{1}\)H MRS data, due to its popularity in clinical application of MRS. We have compared against TARQUIN, as a freely available automatic software package that is widely used in MRS signal analysis applications with better claimed accuracy than the LCModelTM. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Metabolites**} & \multicolumn{2}{c}{**(a)**} & **PCC** & \multicolumn{2}{c}{**(b)**} & **Precuneus** \\ \cline{2-5}  & **Proposed** & **Targuin** & **Proposed** & **Targuin** \\ \hline
**NAA** & \(9.93\pm 1.52\) & \(8.7\pm 1.23\) & \(7.91\pm 0.88\) & \(8.69\pm 0.41\) \\
**Creatine** & \(7.79\pm 0.56\) & \(6.85\pm 0.2\) & \(7.49\pm 0.56\) & \(6.92\pm 0.12\) \\
**Choline** & \(0.79\pm 0.11\) & \(1.04\pm 0.3\) & \(0.82\pm 0.23\) & \(1.03\pm 0.17\) \\
**Myo-inositol** & \(1.84\pm 0.5\) & \(2.07\pm 0.46\) & \(1.67\pm 0.32\) & \(2.02\pm 0.48\) \\
**Gaba** & \(1.95\pm 0.41\) & \(1.34\pm 0.47\) & \(1.46\pm 0.29\) & \(1.44\pm 0.73\) \\
**Lactate** & \(0.56\pm 0.29\) & \(0.2\pm 0.03\) & \(0.56\pm 0.31\) & \(0.52\pm 0.37\) \\
**Glutamate** & \(1.38\pm 0.47\) & \(6.45\pm 0.76\) & \(1.22\pm 0.17\) & \(5.7\pm 1.5\) \\
**Glutathione** & \(0.95\pm 0.33\) & \(1.71\pm 0.16\) & \(0.85\pm 0.25\) & \(1.77\pm 0.13\) \\
**Aspartate** & \(2.09\pm 3.05\) & \(2.19\pm 0.33\) & \(2.8\pm 0.98\) & \(2.34\pm 0.41\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: A comparison between in vivo metabolite concentration calculation in two brain regions (a) Posterior Cingulate Cortex (PCC) and (b) precuneus. Figure 5: **(a)** The fitting in vivo data MR spectra using the TARQUIN; **(b)** the in vivo 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). The complexity of metabolites spectra varies according to their chemical structure. For instance, the NAA spectrum frequently contains one peak that is assumed to N-acetyl aspartate [40]. The Cr peak corresponds to superposition of creatine and phosphocreatine. The PCh spectrum is more complex, containing a contribution from phosphocholine, glycerophosphocholine, free choline, acetylcholine, phosphatidylcholine, and choline-plasminogen [29]. The myo-inositol peak includes phosphatidylinositol, inositol polyphosphatidide, and inositol monophosphate [30; 41]. Therefore, basis sets developed in the environment laboratories must consider all of these contributions carefully, before they can be used to model the MR spectra, through the basis sets methods of MRS signal analysis. One, reason for under/over estimation of metabolite concentration using these methods could be imperfect matching of subpeaks of the complex non-orthogonal basis sets with the corresponding metabolites in the MR spectra. The fitted model using TARQUIN in Figure 4a shows that the NAA and Creatine peaks are not properly detected. TARQUIN estimates the model using the basis sets and then estimates the baseline, which makes the modeling of the metabolite's MR spectra an error prone task. In agreement with some literatures including [1; 10], the baseline is a major source of variability, and therefore it must be detected and corrected before the peak matching step. On the other hand, TARQUIN has a fixed number of basis sets which will be fitted to a spectrum, even if that spectrum does not contain corresponding metabolites, which is a source of error in modeling and quantification of metabolites concentration of the in vitro data. In the proposed approach, the decomposing and clustering process are performed right after the water peak removal.