## 3 Results and Discussion
### Performances Evaluation of \(p\)-DAS on Image Quality
#### 3.2.2 Eleven Plane Wave Imaging  
The results for 11 PW imaging are analyzed in this section. The images obtained on the four phantoms with 11 PW are shown in Figure 5. The measurements are summarized in Figure 6. The results demonstrate that \(p\)-DAS can be applied successfully to plane wave compounding since the effects of \(p\)-DAS obtained with 1 PW are preserved when using 11 PW (i.e., as \(p\) increases, better lateral resolution and CR, but worse CNR). The lateral resolution is improved as \(p\) increases both in simulation (Figure 6b; DAS, 0.62 mm; 2-DAS, 0.49 mm; 3-DAS, 0.44 mm) and experiment (Figure 6f; DAS, 0.65 mm; 2-DAS, 0.51 mm; 3-DAS, 0.44 mm). The CR is also improved for higher \(p\)-values, for both simulation (Figure 6c; DAS, 28.1 dB; 2-DAS, 43.7 dB; 3-DAS, 55.1 dB) and experiment (Figure 6g; DAS, 21.0 dB; 2-DAS, 33.6 dB; 3-DAS, 41.4 dB). In the image (Figure 5e,g,h), the cysts are darker with respect to the speckle when using \(p=2\) or \(p=3\). This can be explained as follows. If the compounding leads to different mean values for each channel, this is because no coherent source is detected, but only noise or interference: the nonlinear weighting attenuates the noisy pixel value. In this way, the interferences from bright speckles in the cysts vanish, so the cysts tend to be darker, and so the CR is improved. As \(p\)-DAS increases the gap between coherent and incoherent sources, the variance inside the cyst and inside the speckle are also increased. Such darkening of the speckle structure is also noticeable on experimental phantoms (Figure 5m,o,p). In this way, the CNR decreases with the \(p\)-values for both simulation (Figure 6d; DAS, 6.5 dB; 2-DAS, 3.0 dB; 3-DAS, 0.1 dB) and experiment (Figure 6g; DAS, 7.7 dB; 2-DAS, 4.1 dB; 3-DAS, 1.3 dB). Finally, the impact of \(p\)-DAS on the axial FWHM is less than with 1 PW, for both simulation (Figure 6a; DAS, 0.40 mm; 2-DAS, 0.39 mm; 3-DAS, 0.38 mm) and experiment (Figure 6e; DAS, 0.56 mm; 2-DAS, 0.55 mm; 3-DAS, 0.54 mm). Indeed, as observed for 1 PW, the more a scatterer is impacted by interference, the more its FWHM is improved. However, as the compounding of the 11 PW before _p_-DAS attenuates the level of interference, the nonlinear behavior of _p_-DAS with respect to the amplitude is less highlighted.  
In summary, _p_-DAS is an interesting beamformer to reject any incoherent pixel values that result from either ill rephased wavefronts, or waveforms corrupted by interference or noise. This explains the better lateral resolution and enhanced side-lobe rejection, and so the improved contrast ratio. These three first metrics increase with the _p_-value. However, the CNR is degraded, as the speckle results from interference, and so it is heavily rejected with respect to the coherent target. Finally, _p_-DAS appears to be a good candidate to resolve particularly punctual targets embedded in speckle or noise.  
Figure 5: B-mode images obtained with eleven plane wave imaging for the four phantoms and the four beamformers compared: DAS (**a**,**e**,**i**,**m**), FDMAS (**b**,**f**,**j**,**n**), 2-DAS (**c**,**g**,**k**,**o**), and 3-DAS (**d**,**h**,**l**,**p**). (**a**–**d**) the numerical phantom used for the resolution; (**e**–**h**) the numerical phantom used for the contrast; (**i**–**l**) the experimental phantom used for the resolution; and (**m**–**p**) the experimental phantom used for the contrast. All of the images are displayed with 60-dB dynamic range.