# A Spatial Compounding Method for Non-Delayed Sequential Beamforming
## 4 Discussion  
This paper exploits a spatial compounding method for non-delayed sequential beamforming. Our proposed method depends on theoretical modeling of the transmit pressure field. As a result, two beamformed images originated from two ends of the transmit aperture can be produced using the same received signals. From the in vitro results, our proposed compounding images significantly improve the image contrast without sacrificing the resolution. In vivo studies also demonstrate the robustness of our proposed compounding methods. Image contrast is greatly enhanced in both the longitudinal and cross-section carotid artery images.  
The aim of NDSB is to simplify the front-end architecture and retain the beamformer's quality comparable to DRF. The image quality is highly affected by the transmit F#: smaller F# results in better resolution and contrast. Small F# means larger transmit opening angle. This ensures more data in the low-resolution image can be synthesized to generate a pixel point in the high-resolution image. The optimal F# is set to 0.75 in [13]. With this setting, degrading lateral resolution is found at shallow depth (\(<\)40 mm) and inferior contrast (CR, CNR) compared with DRF.  
In this work, the transmit F# is also 0.75. NDSB produces inferior image quality (lateral resolution, CR, CNR) compared to DAS. This conclusion is the same in [13]. The proposed compounding improves the resolution and image contrast by summation of limited-correlated images. The effect of transmit F# to the compounding method is illustrated in Figure 9. Two transmit F# are compared: 0.75 and 3. To measure the lateral  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **DAS** & **NDSB** & **Comp1** & **Comp2** \\ \hline CR [dB] & \(-13.5\) & \(-15.1\) & \(-7.8\) & \(-7.1\) \\ CNR [dB] & 10.8 & 7.7 & 11.3 & 12.2 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Contrast-ratio and Contrast-to-noise ratio for Figure 8.  
Figure 8: B-mode images of the longitudinal-section carotid artery in 50-dB range. (**a**) DAS image (**b**) NDSB image (**c**) Comp1 image (**d**) Comp2 image.  
resolution, the same point target in Figure 4 is used. The result is shown in Figure 9a. The y-label is the ratio of lateral resolution of NDSB, Comp1, and Comp2 to that of DAS in certain transmit F#. When the F# increases, the lateral resolution of the compound method degrades. To address the image contrast, we image the carotid artery same in Figure 7. The ratio of CR and CNR (to that of DAS) in terms of transmit F# is plotted in Figure 9b. We can find the same conclusion: when F# increases, the image contrast also degrades. This is easily understood: a larger F# means a smaller active aperture given the same focus depth. The transmit origins for the contributing signal get closer and the beamformed images carry almost the same spatial frequencies. The summation of these images gives limited improvement compared with a small F# (larger active aperture). The computation time to reconstruct an image of 30 mm \(\times\) 30 mm is 7.2 s for DAS, 8.5 s for NDSB, 18.5 s for Comp1, and 19.2 s for Comp2.