## 3 Results
### Compared with Compressive Beamformer in the Temporal Domain  
To analyze the performance of compressive beamforming method in the wavenumber domain based on [PERSON]'s f-k migration (fkCS), we compared the new framework with the conventional beamforming based on compressed sensing in the temporal domain. To reduce the influence of different beamformers on image quality, the algorithm of control group still uses [PERSON]'s f-k migration during beamforming, but the compressed sensing is applied to the echo signal before FFT, which means the signal in the temporal domain is compressed. This framework of the control group is called beamformer in the temporal domain based on compressed sensing (abbreviated as tmCS). The lateral resolution and contrast were calculated by the simulated data at different compression rates. The compression rate decreases from 100% to 20% to analyze the changes of the lateral resolution and contrast. The B mode images after two kinds of beamformers are shown as Figure 7d,e, whose compression rate is 50%.  
With the decrease in compression rate, the beamformer will take up less memory and less transmission space. However, the information will be lost as well. From B mode images generated by fkCS in Figure 7d and by tmCS in Figure 7e with a dynamic range of 50 dB, artifacts appear due to the loss of information with the compression rate of 50%. It can be seen from the B-mode images that at a compression rate of 50%, the image quality of fkCS is significantly better than that of tmCS. As shown in Figure 7e, when the amount of the signal is compressed to 50%, the low echo signal will be almost covered and the high intensity signal will produce artifact. Since the image of tmCS loses half of the signal during the compression process in the temporal domain, it is more dependent on the nearby signal when the reconstruction algorithm restores the image. Thus, the low-echo signal will be covered by the surrounding signal, and the high-intensity signal will affect the surrounding signal and produce artifacts. In the Fourier domain, due to the symmetry of the Fourier-transformed signal, the signal can retain more effective information during compression and reduce the generation of noise and artifacts during reconstruction of signal.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **gCNR** & \\  & **Hypoechic** & **Bright Region** \\ \hline DAS & 0.8429 & 0.9385 \\ fk & 0.9035 & 0.8874 \\ fkCS\_80\% & 0.8529 & 0.8917 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Contrast of DAS, [PERSON]’s f-k and proposed framework.  
Figure 6: Effect of depth on the lateral resolution.  
Figure 7c shows effects of compression rate on lateral resolution. In order to reduce the influence of artifacts of strong reflection area, we choose the point scatterer at (10, 45) mm to measure resolution. From Figure 7c we can see that the lateral resolutions are comparable when the compression rate is above 70%. When the compression rate decreases sequentially, the FWHM of tmCS increases rapidly, while the resolution of fkCS fluctuates slightly. The image quality of tmCS deteriorates more rapidly because more information is lost during compression than that in fkCS.