# Adaptive Beamformer Combined with Phase Coherence Weighting Applied to Ultrafast Ultrasound
## 3 Results  
### Basic Experimental Results Using Phantom  
Figure 2a-d show B-mode images of a string phantom obtained by the conventional DAS beamforming, the mAPES beamforming without gPCF, and those with gPCFs estimated before and after applying the adaptive beamformer weights, respectively. In the phantom used for this experiment, three point targets were placed at different axial depths. Figure 3a,b show the lateral amplitude profiles with respect to point targets at axial depths of 12 mm and 22 mm in Figure 2a-d.  
Figure 3: Lateral amplitude profile obtained from point target at axial depths of (**a**) 12 mm and (**b**) 22 mm in Figure 2.  
Figure 2: B-mode images of string phantom obtained (**a**) with delay-and-sum (DAS); (**b**) with modified amplitude and phase estimation (mAPES) beamforming without gPCF, and mAPES beamforming with gPCFs evaluated (**c**) before and (**d**) after applying the adaptive beamformer weights. In Figure 3a,b, the lateral amplitude profile obtained with the proposed method was sharpened and speckles obtained with the proposed method were resolved as compared to those obtained with the conventional mAPES beamformer. The lateral full widths at half maxima of the lateral amplitude profiles shown in Figure 3a obtained by DAS, mAPES without gPCF, and those with gPCFs estimated before and after applying the adaptive beamformer weights were 0.560, 0.392, 0.356, and 0.344 mm, respectively. Also, the lateral full widths at half maxima of the lateral amplitude profiles shown in Figure 3b obtained by DAS, mAPES without gPCF, and those with gPCFs estimated before and after applying the adaptive beamformer weights were 0.668, 0.348, 0.288, and 0.288 mm, respectively. Figure 4a,b show that the phases of the outputs of the sub-aperture beamformers before and after applying the adaptive beamformer weights, respectively, which was obtained at range and lateral positions of 22 mm and 3.60 mm, respectively. These results show that the phases shown in Figure 4b deviate among the sub-apertures, whereas those shown in Figure 4a were well aligned. Figure 5a-d show B-mode images of a cyst phantom obtained by the DAS beamforming, the mAPES beamforming without the gPCF, and those with the gPCFs estimated before and after applying the adaptive beamformer weights, respectively. Figure 4: Phase of the signal obtained by each sub-aperture element (**a**) before and (**b**) after applying the adaptive weights. Figure 5: B-mode images of cyst phantom obtained (**a**) with DAS; (**b**) with mAPES beamforming without gPCF, and mAPES beamforming with gPCFs evaluated (**c**) before and (**d**) after applying the beamformer weights. In this experiment, an anechoic cyst was embedded in the phantom. A rectangular region (from 16.8 to 19.2 mm in the range direction, from 9 to 11 mm in the lateral direction) was regarded as the lesion, and another rectangular region (from 16.8 to 19.2 mm in the range direction, from 5 to 7 mm in the lateral direction) was regarded as background. Contrasts of the B-mode image obtained by DAS, mAPES without gPCF, and those with gPCFs estimated before and after applying the adaptive beamformer weights were 4.05, 5.14, 5.61, and 5.32 dB, respectively. Experimental results show that image contrast was improved by the proposed method. Figure 6a,b show B-mode images of the wire phantom and the cyst phantom obtained by the adaptive beamforming combined with the PCF estimated without the sub-aperture beamforming. In Figure 6a,b, the gPCF was estimated before applying the adaptive beamforming weights. The lateral full widths at half maxima of point targets at depths of 12 mm and 22 mm in Figure 6a were 0.356 mm and 0.280 mm, respectively, and the contrast of the B-mode image in Figure 6b was estimated to be 5.99 dB.