## 3 Results  
### Compared with [PERSON] and [PERSON]'s f-k Method  
To analyze the performance of the new beamforming method in B mode ultrasound imaging, the point scatterers at different depth were used to calculate resolution, and the hypoechoic region centered at (\(-\)5, 40) mm and the strong reflected regions centered at (\(-\)5, 70) mm were used to calculate different kinds of contrast. As it shows in Figure 4, the 6 mm radius cyst called region A is used to analyze the contrast of hypoechoic. The region B with 6 mm diameter is used to analyze the contrast of strong reflected region. Region C in the red square is used as the background to calculate the contrast. The horizontal resolution is analyzed by the point scatterer at different positions. After evaluating the performance of the algorithm in simulation, the in vivo plane wave measurements were executed by Verasonics research scanner (Vermon Inc., Tours, France) in Section 4. The contrast was represented by gCNR, which was defined as [37]  
\[\mathrm{gCNR}=1-\int_{-\infty}^{\infty}\min_{x}\{p_{t}(x),p_{b}(x)\}dx \tag{21}\]  
where \(p_{t}(x)\) is the probability density distribution in the target region A and region B, and \(p_{b}(x)\) is the probability density distribution of background region C.  
The performance of wavenumber domain beamforming is evaluated in two aspects. The first is to compare the image quality with DAS. The second part is to compare the image quality with strictly consistent condition and the same compressed rate, so as to assess the stability of the algorithm and the performance of compressed sensing in the wavenumber domain compared with that in the temporal domain. Multi-angle RF coherent compounding can be applied on both DAS and beamforming in the wavenumber domain to further improve image quality. However, in order to eliminate the influence of the number of angles on the image quality, we simulated only one plane wave on angle 0\({}^{\circ}\) to perform different beamforming algorithms in this section. We compared the compressive beamforming with [PERSON]'s f-k migration (represented by fkCS in the image) with DAS to evaluate the performance of the new process by image quality, as well as compared with non-compressive framework. In Section 3.1, the image quality was evaluated and compared with the compression rate \(R=80\%\) in fkCS (abbreviated as fkCS_80%), and the simulated result is shown in Figure 5 with a dynamic range of 50 dB. The compression rate is defined as  
\[R=\frac{N_{c}}{N_{o}}\times 100\% \tag{22}\]  
where \(N_{c}\) and \(N_{o}\) are the amount of data after and before compressed sensing, respectively. In this part, the image quality is evaluated from different views. Firstly, the lateral resolution is measured at different depths. Secondly, the contrast of cyst and high reflection region are calculated and represented by \(gCNR\). The point scatterers in the region D at the depth from 30 mm to 85 mm were involved to analyze the lateral resolution at different depths. The lateral resolution was estimated by measuring the full-width at half maximum (FWHM) of the envelop of the signal after beamforming. The effect of different depths on lateral resolution with different beamformers is shown in Figure 6. As shown in Figure 6, the compressive beamforming in the wavenumber domain provides comparable or better lateral resolution than DAS, when the data load has been compressed to 80%, especially with increase of the depth. In this study, we use dynamic aperture in the DAS beamformer with Hanning window to improve the lateral resolution in near field. However, the resolutions of DAS in near field still not match that of fkCS, whose compression rate is 80%. With the depth increase, the resolutions of three imaging method are comparable, but the resolutions vary in deep place. Consequently, lateral resolution of beamformer in the Fourier domain perform better in near field and deep place.