## 4 Discussion  
In this study, the CSAKC technique was proposed to reduce ringing and/or blurring artifacts caused by the undersampling pattern in CSA techniques. A previous study found that aliasing artifacts could occur when using the CSAKS technique to obtain high temporal and spatial resolution [23]. Therefore, the CSAKC technique was developed to reduce  
Figure 4: Mean line profiles and modulation transfer function (MTF) curves of CSA images with 25% undersampling ratio in the brain phantom. (**a**) CSAM, CSAKS, and CSAKC images and ROIs selected for further analysis; (**b**) the mean line profiles of each CSA image within the ROI; (**c**) MTF curves of each CSA image. The line pairs per millimeter (lp/mm) were lowest for CSAM, followed by CSAKS and CSAKC for the same relative MTF value, suggesting that CSAKC showed the best contrast between tissues. Figure 5: Visual comparison of a full k-space image and CSAK images in a human subject. Although CSAK images were acquired with the same undersampling ratio, the ringing artifacts only occurred when using CSAKS. Note that the acquisition times of the full k-space and CSAK images were 5 m 56 s and 5 m 5 s, respectively. artifacts while maintaining the acquisition time and was evaluated using in vivo human imaging, simulation, and phantom experiments. The results showed reduced ringing and image blurring artifacts. Through the simulation results, we found a decreased SNR as the number of sampling lines increased during high-resolution imaging. According to Equation (1), when the pixel size of the k-space (\(\Delta\)k) increases, the field of view (\(FOV\)) can decrease in the image domain, but when the \(FOV\) is fixed, the SNR increases because of the reduction in phase-encoding lines (\(N_{y}\)), which can eventually increase the pixel size (\(\Delta y\)) in the image space through k-space undersampling (Equation (2)). \[\Delta\kappa\propto\frac{1}{FOV} \tag{1}\]  
\[\text{SNR}\propto FOV_{y}\sqrt{\frac{1}{N_{y}}} \tag{2}\]  
There were no artifacts in the full k-space sampling for in vivo human imaging, but undersampling simulation images generated from the full k-space dataset demonstrated ringing and blurring (Figure 2). Furthermore, this study also used the brain phantom to investigate whether aliasing in CSA images was an artifact caused by motion or by a lack of sampling lines. The results showed that the smaller the number of sampled lines (i.e., 25%), the greater the number of artifacts. As a result of the analysis, we found that no artifacts occurred in images with full k-space sampling, but that aliasing occurred according to the undersampling ratio even in a motionless brain phantom. This can be interpreted as the result of insufficient k-space sampling numbers, not motion. Furthermore, although CSAKC required a shorter acquisition time, it had no image blurring and a high signal intensity compared with a full k-space image (Figure 5). Based on these results, it is expected that the proposed technique can be utilized as a method that does not generate artifacts while increasing temporal and spatial resolution. In future studies, it will be necessary to develop a method to reduce the noise generated in the CSAKC method, since the SNR for high-resolution imaging was still insufficient. In addition, it is necessary to compare and analyze the efficacy of the CSAKC method with changes in the SNR according to the magnetic field, by obtaining an image to which this technique is applied at an ultra-high magnetic field strength of 7T. More importantly, it is necessary to further compare the reconstructed images with the acquired real image, since there is a possibility that the acquired phases may be different due to environmental factors such as temperature. In addition, the proposed method should be further evaluated with more subjects, and further quantitative evaluations and technical improvements should be sought, including radially randomly undersampled CSA techniques and temporally rather than spatially randomized CSA techniques.