# Free-Breathing and Ungated Cardiac MRI Reconstruction Using a Deep Kernel Representation
## 4 Experiments Setup  
### Acquisition Scheme and Pre-Processing of Data  
In this work, we use the short-axis orientation without a contrast agent to showcase the results. Five subjects were involved in this study, and the public information of these five subjects, including the average heart rate, are shown in Table 1. All the data were acquired on a 3T MR750W scanner (GE Healthcare, Waukesha, WI, USA). The data were acquired using a 2D gradient echo (GRE) sequence with golden angle spiral readouts in a free-breathing and ungated fashion. Some sequence parameters include: FOV = 380 mm \(\times\) 380 mm; TR = 8 ms; flip angle = 14\({}^{\circ}\); slice thickness = 8 mm; readout bandwidth = 500 Hz. The reconstruction matrix size is 340 \(\times\) 340. All the data was acquired using the AIR coil developed by GE HealthCare (Waukesha, WI, USA). We used an in-house algorithm to pre-select the coils that provide the best signal-to-noise ratio in the region of interest. We then estimated the coil sensitivity maps based on these selected channels using ESPIRiT [35] and assumed them to be constant over time. For each slice, a total number of 950 spirals were acquired. During the reconstruction, the first 200 spirals were deleted. For the rest of the 750 spirals, we bin every five spirals corresponding to 40 ms temporal resolution for each frame in the time series.  
For the comparison purpose, the conventional 2D photoplethysmography (PPG) gated breath-hold images using the balanced steady-state free precession (bSSFP) sequence were also acquired for all the slices. PPG is a simple optical technique used to detect volumetric changes in blood in peripheral circulation and hence can be used as one of the choices for monitoring the cardiac cycle. Balanced steady-state free precession sequence is one type of gradient echo pulse sequence in which a steady, residual transverse magnetization is maintained between successive cycles. For each subject, the breath-hold images of a middle slice were also acquired using a fast gradient echo (FGRE) sequence for comparison. The acquisition scheme for FGRE is Cartesian,  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Sex** & **Age** & **Health Condition** & **Avg. Heart Rate (bpm)** \\ \hline Subject 1 & F & 29 & Healthy & 64 \\ \hline Subject 2 & M & 51 & Healthy & 71 \\ \hline Subject 3 & M & 20 & Lower LVEF and RVEF & 88 \\ \hline Subject 4 & F & 26 & Healthy & 65 \\ \hline Subject 5 & F & 24 & Lower heart rate; Lower RVEF & 54 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Public information of the five subjects involved in this work.  
while the spiral GRE sequence in the proposed acquisition scheme uses the spiral trajectories, which is non-Cartesian. The parameters for the breath-hold bSSFP sequence were: FOV = 380 mm \(\times\) 380 mm; spatial resolution = 0.74 mm \(\times\) 0.74 mm; TR/TE = 3.5/1.5 ms; flip angle = 49\({}^{\circ}\); slice thickness = 8 mm; readout bandwidth = 488 Hz. The parameters for the breath-hold FGRE sequence were: FOV = 380 mm \(\times\) 380 mm; spatial resolution = 1.48 mm \(\times\) 1.48 mm; TR/TE = 5.1/2.8 ms; flip angle = 15\({}^{\circ}\); slice thickness = 8 mm; readout bandwidth = 488 Hz.