## 4 Results  
### Simulations  
#### 4.1.1 Simulated Phantom with Point Targets  
The proposed CPWC+NSVD method was compared to CPWC and CPWC+SVD. Images obtained using adaptive weighting factors (CF, GCF, and SLSC) to weight the output of CPWC were also presented as a comparison of the adaptive weighting methods based on NSVD. For convenience, hereinafter, CPWC weighted by CF, GCF, and SLSC are referred to as CF, GCF, and SLSC, respectively.  
The first simulated phantom contains several point targets from a depth of 10 mm to 45 mm. Figure 1 presents B-mode images beamformed using different methods. The top row contains CPWC, CPWC+SVD, and CPWC+NSVD images. The second and third rows contain CF-, GCF-, and SLSC-weighted CPWC images and weighted images with the NSVD filter for \(\beta=2\) and \(\beta=3\). Figure 2 shows the zoomed images of the point target located at a depth of 20 mm with a dynamic range of 80 dB. CPWC shows the highest noise and sidelobe levels. Through the use of the NSVD filter, noise is suppressed in the images of Figure 1d-e and Figure 2d-e, while sidelobes of NSVD+CPWCshow little suppression compared to CPWC. It is also noted that the adaptive weighting methods can reduce noise and sidelobes relative to CPWC, CPWC+SVD, and CPWC+NSVD. Lateral profiles of two-point targets \(p_{1}(x,z)=(0\) mm, 20 mm) and \(p_{2}(x,z)=(0\) mm, 40 mm) in all simulated images are shown in Figure 3. For adaptive weighting methods, the NSVD filter leads to increased sidelobes, which is obvious in CF-weighted images. After further observations, NSVD+CPWC shows reduced sidelobes compared to CPWC and CPWC+SVD in Figure 2b. Therefore, NSVD may have a good ability to suppress sidelobes in the deep region. It is also observed that beamformers with \(\beta=3\) provide narrower mainlobes than those with \(\beta=2\).  
The lateral FWHM of point targets \(p_{1}(x,z)=(0\) mm, 20 mm) and the average FWHM of all simulated point targets are calculated and Figure 4 gives the barplot of lateral FWHM. As seen in Figure 4, the NSVD filter has little effect on lateral FWHM. Compared to CPWC, CPWC+SVD (\(\beta=2\)) and CPWC+NSVD (\(\beta=2\)) have a slightly larger lateral FWHM, while CPWC+SVD (\(\beta=3\)) and CPWC+NSVD (\(\beta=3\)) have equivalent lateral FWHM values. For adaptive weighting methods, \(\beta=2\) also leads to a wider lateral FWHM.  
Figure 1: B-mode images of simulated phantom with point targets formed by different methods. (**a**) CPWC, (**b**) CPWC+SVD (\(\beta=2\)), (**c**) CPWC+SVD (\(\beta=3\)), (**d**) CPWC+NSVD (\(\beta=2\)), (**e**) CPWC+NSVD (\(\beta=3\)), (**f**) CF, (**g**) GCF, (**h**) SLSC, (**i**) CF+NSVD (\(\beta=2\)), (**j**) GCF+NSVD (\(\beta=2\)), (**k**) SLSC+NSVD (\(\beta=2\)), (**l**) CF+NSVD (\(\beta=3\)), (**m**) GCF+NSVD (\(\beta=3\)), (**n**) SLSC+NSVD (\(\beta=3\)).  
Figure 4: Lateral full width at half maximum (FWHM) in simulated images: (**a**) \(p_{1}(x,z)=(0\;\mathrm{mm},20\;\mathrm{mm})\), (**b**) average values and standard deviation of all point targets.  
Figure 2: Simulated point target images formed by different methods and displayed with a dynamic range of 80 dB. (**a**–**n**) Zoomed images of the point target at a depth of 20 mm in Figure 1a–**n**, respectively.