## 4 Results
### In Vivo Brain  
The reconstruction results for an _in vivo_ 4D EP-COSI brain scan of a healthy 23 year old male are shown in Figure 4. A representative 2D COSY spectrum was chosen from a central 2 \(\times\) 2 \(\times\) 2 cm\({}^{3}\) voxel of the brain that shows each of the metabolites of interest with low fat and water contamination, as illustrated by the green square on the T1-weighted image in the bottom left of Figure 4. The fully sampled spectrum in the top left corner of the figure was under-sampled 8\(\times\) using the sample mask from Figure 3, then reconstructed by CS, TV, MaxEnt, GS\({}_{1}\), and GS\({}_{2}\) as shown. As is seen in Figure 2, the 8\(\times\) NUS spectrum shows significant aliasing of the diagonal peaks along \(F_{1}\) and a collapse of the peaks within the \(F_{1}\) projection. The CS and TV reconstructions have higher noise floors than the other reconstructions and narrower line widths, as can be seen at the base of each diagonal peak. The GS reconstructions produced the most accurate reconstructions of the peak line widths and were able to maintain the noise level. The NAA and Glx cross peaks can be partially seen in each of the reconstructions; however, they are obscured by noise in the CS and TV reconstructions and have low amplitudes in the MaxEnt and GS\({}_{1}\) reconstructions. GS\({}_{2}\) was able to reconstruct the cross peaks to a reasonable degree in spite of the large water tail along \(F_{1}\) at \(F_{2}=\) 4.72 ppm that nearly obscured the lower NAA cross peak. \begin{table}
\begin{tabular}{l c c} \hline \hline  & \(F_{1}\) (ppm) & \(F_{2}\) (ppm) \\ \hline
**Diagonals:** & & \\
**Cho** & 3.1–3.4 & 3.1–3.4 \\
**Cr303** & 2.9–3.1 & 2.8–3.2 \\
**Cr391** & 3.8–4.1 & 3.7–4.1 \\
**Glx** & 2.4–2.6 & 2.3–2.5 \\
**Lac** & 1.1–1.7 & 1.0–1.6 \\
**mI** & 3.5–3.8 & 3.4–3.7 \\
**NAA** & 1.7–2.3 & 1.7–2.1 \\
**Cross Peaks:** & & \\
**Glx (Lower)** & 1.7–2.2 & 3.4–4.1 \\
**Glx (Upper)** & 3.4–3.9 & 1.7–2.4 \\
**NAA (Lower)** & 2.0–3.0 & 4.0–4.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: \(F_{1}\),\(F_{2}\) ppm ranges used to calculate the metabolite RMSEs shown in Figure 3.  
Figure 5 shows the spatial distribution of a 1.5 \(\times\) 1.5 ppm region of a 2D COSY spectrum centered at \(F_{2}\) = 2.5 ppm taken from each voxel of the fully sampled, 8\(\times\) NUS, and reconstructed _in vivo_ 4D EP-COSI brain scan shown in Figure 4. The fully sampled data is superimposed onto a T1 weighted image from the middle of the EP-COSI slice that was acquired during the same study. Each spectral region contains the metabolite diagonals and cross peaks of NAA/NAAG and Glx in that region. The acquisition VOI used during the scan is shown as the white bolded line in the fully sampled image on the left and the black bolded line in the images on the right. The contour levels used for the fully sampled spectra were used for the 8\(\times\) NUS and reconstructed spectra. As can be seen, the NAA/NAAG and Glx peaks are well resolved within the VOI of the fully sampled image with minimal spatial aliasing along \(Y\) and noticeably more aliasing along \(X\), which was caused by the PSF of the EP-COSI pulse sequence. The peak amplitudes of the NAA/NAAG and Glx peaks are roughly equivalent over the VOI, with the exception of reduced peak amplitudes in the anterior-left and posterior-right voxels. The 8\(\times\) NUS metabolite peak amplitudes are lower than in the fully sampled image, a trend also seen in Figures 2 and 4, and the increased spatial aliasing along \(Y\) is evident from the presence of NAAG and Glx peaks outside of the VOI. The CS and TV reconstructions show increased noise both inside and outside of the VOI, with CS failing to properly reconstruct many of the peaks in the posterior row of the VOI with the \"choppy\" line shapes that were seen in Figures 2 and 4. The MaxEnt reconstruction shows better denoising properties than the CS and TV reconstructions with most of the NAA/NAAG and Glx peak amplitudes and line widths restored within each voxel of the VOI.