# Adaptive Beamformer Combined with Phase Coherence Weighting Applied to Ultrafast Ultrasound
## 4 Discussion  
In the present study, we tried to combine the modified adaptive beamformer with the phase coherence weighting. From the experiments using a wire phantom, the lateral full width at half maxima obtained by the proposed method was better than conventional DAS beamforming and adaptive beamforming only. Also, in a B-mode image shown in Figure 2c, the speckles in diffuse scattering medium in the axial deep region were more clearly resolved than in Figure 2b. Furthermore, as shown  
Figure 8: B-mode images of carotid artery obtained (**a**) with DAS; (**b**) with mAPES beamforming without gPCF, and those with gPCFs estimated (**c**) before and (**d**) after applying the beamformer weights. Figure 7: Changes in (**top**) lateral full widths at half maxima and (**bottom**) peak-to-speckle ratio obtained by the proposed method with gPCF estimated before applying the adaptive beamformer weights. Results were obtained with respect to point targets at axial depths of (**a**) 12 mm and (**b**) 22 mm. in Figures 2c and 6a, obtained results show that the visibility of echoes from diffuse scattering medium was significantly improved by applying the gPCF to the outputs of the sub-aperture beamformers. In the present study, we also tried to estimate the PCF using the phase variance of the outputs of the sub-aperture beamformers, which were subjected to the weight vector determined by the mAPES beamformer. In such a case, as shown in the B-mode image in Figure 2d, the spatial resolution became worse as compared to that shown in Figure 2c, in which the PCF was estimated from the outputs of the sub-aperture beamformers before applying the adaptive weights. The mAPES beamformer changes the amplitude and phase of the outputs of the sub-aperture beamformers adaptively so that the lateral resolution is optimized. In Figure 4a,b, obtained results show that the phase rotation was induced by the adaptive beamformer weights even with the echo signals from a strong scatterer and, therefore, the gPCF became low. With respect to the point target at an axial depth of 12 mm, a point scatterer depicted in Figure 2d was blurred as compared to that depicted in Figure 2c. This is because the peak value of the echo from the point scatterer decreased by the gPCF from echo signals after adaptive weighting but the phase variance of the signals other than the peak position is originally large and adaptive weights do not change the gPCF value significantly. From the experimental results on a cyst phantom, which are shown in Figure 5a-d, image contrast was improved using the gPCF estimated before and after applying the adaptive beamformer weights. Both the adaptive beamformer and the PCF were proposed for improvement of the spatial resolution but improvement of contrast was accomplished by applying the gPCF to the output of the modified adaptive beamformer. From the experimental results on two phantoms, the gPCF evaluated using echo signals subjected to mAPES beamformer weights was shown to give worse results than that evaluated using echo signals without mAPES beamformer weights. Consequently, evaluating the gPCF using echo signals subjected to adaptive beamformer weights is not preferred. In the B-mode images in Figure 2, a point target at a depth of about 7 mm is somewhat blurred also in the B-mode image obtained by DAS beamforming (Figure 2a). In the near field, the ultrasound field fluctuates significantly due to interference among ultrasonic waves emitted from the transducer [38], and the performance of image formation is degraded. The performance of the proposed method could be degraded because such interference would also affect the proposed method, which uses the amplitude and phase information of the measured ultrasonic signal. Therefore, we need more improvements in the beamformation process for near-field imaging.