## 5 Discussion  
### Comparision of SCF-Based Beamformers Performance  
The image results (simulation, phantom and in vivo) show that the uSCF beamformer offers improvements over the conventional DAS, sSCF and aSCF beamformers. To further illustrate the proposed method, we present the CR and gCNR in simulation (35-mm-depth cyst) as a function of the number of transmitted plane waves, varying from 1 to 11. As shown in Figure 8, both the CR and gCNR increase with the number of angles for all the methods, and the uSCF performs best at all numbers of the angles. We also note that uSCF and aSCF 'degenerate' to the same as sSCF and DAS, respectively, under the premise of single-angle plane waves (0\({}^{\circ}\)). It is due to the lack of angular coherence, which could also be deduced from the Equations (14) and (18).  
The improvements of uSCF could be explained by two reasons. First, uSCF uses both the spatial coherence factor (sSCF) and angular coherence factor (aSCF). The two coherence factors could be combined to further improve image quality. Second, uSCF calculates the coherence factor from all the elements in \(X\)(k) (4), which helps to improve the accuracy of the estimation. The cyst results in the simulation, phantom and in vivo show that the uSCF beamformer offers improvements to suppress noise over the other beamformers.  
SCF-based beamformers are obtained from the phase diversity to discriminate the signals from the noise. The simulation and experimental results show that the SCF-based beamformers offer significant improvements over DAS.  
The improvements of sSCF mainly come from the spatial coherence within each plane wave. Based on the acoustic reciprocity theory, [PERSON] et al. proved its validity [PERSON] et al. (2019). However, the sSCF  
Figure 8: (a) CR and (b) gCNR as a function of the number of angles.  
ignores the angular coherence among the different transmits, thus causing its performance to be lower than the uSCF.  
The images produced with an aSCF beamformer on simulation and experiment data show good agreement with those produced with the sSCF beamformer, which is similar to the results of Li [20]. Based on the acoustic reciprocity, Li proved its validity with respect to the angular coherence of ultrasound, also significantly reducing computational costs.  
However, the decrease in the improvement effect of aSCF from the in vivo data may be explained by the phase shift caused by tissue motions. There will be a longer time interval between the first and last plane wave of a compounded image than the time between the 'adjacent' plane wave. The biological motion may cause phase shift during the time [30], and it causes lower cross-correlation coefficient values between different angles. Because aSCF only use the coherence among the angles, it performs worse than the sSCF and uSCF. Meanwhile, uSCF takes use of both the angular and spatial coherence, and it still performs best when the angular coherence has limited promotion effect. The result of in vivo data proves the effectiveness and robustness of uSCF from the side.  
These results clearly suggest that the SCF beamformers in CPWC should be calculated from data before superposition among all the angles, which is in the approach of uSCF.