# Free-Breathing and Ungated Cardiac MRI Reconstruction Using a Deep Kernel Representation
## 5 Results
### Comparisons with Current Kernel Method  
In this part, we compare the reconstructed images using both the proposed deep kernel method and the SToRM method, which is a state-of-the-art kernel method. Figure 7 showed the visual comparison of the reconstructed images using the two methods. The end-diastolic and the end-systolic phases from two slices were shown in the figure. From the figures, we can see that the proposed deep kernel scheme can reduce the blurring and the motion artifacts in the reconstructed images compared to the images obtained from the SToRM method. This enables us to see more heart details in the reconstructed images. For example, we can see the papillary muscles and the RV free-wall more clearly in the reconstructed images using the deep kernel method. Figure 6: Comparison of image quality of the free-breathing images and breath-hold images. Image quality assessment is done in a blinded fashion by two medical experts. We reconstructed all the short-axis slices acquired from five subjects. We also acquired the fully-sampled breath-hold images for all the slices using the bSSFP sequence. For each subject, we scanned one middle slice using the product FGRE sequence provided by GE HealthCare. The free-breathing images from all the slices received an average score of 2.7, and the clinical fully-sampled images using the bSSFP sequence got an average score of 3.6. The fully-sampled breath-hold images acquired using the FGRE sequence received an average score of 2.9, and the free-breathing images corresponding to these five slices got an average score of 2.8. From which we can see that the reconstructed free-breathing images have similar image quality as the fully-sampled breath-hold images acquired using the product FGRE sequence, even though the images were highly undersampled and acquired in a free-breathing and ungated fashion. The improved image quality from the proposed method was also confirmed by the quantitative results, which were shown in Figure 8. The SNR and CNR calculations were done using Matlab 2019a. We manually chose the regions (region of interest and the noise region) for the calculation. For the SNR calculation, we choose a \(15\times 15\) square region in the left ventricle as the region of interest and a \(25\times 25\) square region out of the body as the noise region. For the CNR calculation, we choose two \(10\times 10\) square regions in the left ventricle as the regions of interest and a \(25\times 25\) square region out of the body as the noise region. From the quantitative results, we can see that the reconstruction from the proposed method is more accurate than the reconstruction from the proposed method. \begin{table}
\begin{tabular}{c c c c c c} \hline  & & **Subject 2** & **Subject 3** & **Subject 4** & **Subject 5** \\ \hline \multirow{2}{*}{LVEF} & Free-breathing & 55.9\% & 47.3\% & 62.6\% & 59.5\% \\  & breath-hold & 56.3\% & 41.4\% & 61.7\% & 58.8\% \\ \hline \multirow{2}{*}{RVEF} & Free-breathing & 56.5\% & 29.6\% & 49.0\% & 39.4\% \\  & breath-hold & 55.8\% & 27.8\% & 49.5\% & 37.0\% \\ \hline \multirow{2}{*}{LVEDV} & Free-breathing & 136 & 169 & 123 & 126 \\  & breath-hold & 142 & 157 & 115 & 119 \\ \hline \multirow{2}{*}{LVESV} & Free-breathing & 60 & 89 & 46 & 51 \\  & breath-hold & 62 & 92 & 44 & 49 \\ \hline \multirow{2}{*}{RVEDV} & Free-breathing & 170 & 145 & 102 & 99 \\  & breath-hold & 156 & 151 & 97 & 81 \\ \hline \multirow{2}{*}{RVESV} & Free-breathing & 74 & 102 & 52 & 60 \\  & breath-hold & 69 & 109 & 49 & 51 \\ \hline \end{tabular}
\end{table} 
Table 2: LVEF and RVEF comparison. Since bulk motions were introduced during the data acquisition of subject #1 and we do not have the matching breath-hold and free-breathing slices for this subject. Therefore, the LVEF and RVEF are compared based on only four subjects. The LVEF calculated from the free-breathing and ungated images and the LVEF calculated from the fully-sampled breath-hold images have a \(p\)-value of 0.295.