## 5 Discussion  
Here, we proposed a neighborhood singular value decomposition (NSVD) filter and its combination with adaptive weighting methods for CPWC to improve imaging performance (noise reduction and speckle pattern preservation). The center-surround relation is useful since the surrounding region has more correlations and gives more useful clues for an imaging point. NSVD considers information of the neighbor region instead of the entire region so that it can more accurately reserve effective signals and reduce noises. The main characteristic of the NSVD filter is  
Figure 16: Barplot of (**a**) CR, (**b**) CNR, (**c**) gCNR, (**d**) sSNR calculated for different method with the in vivo datasets. that it uses a sliding rectangular window to slice the entire region into several continuous sub-regions, then performs SVD for all sub-regions. The sliding window can be viewed as a smoothing filter with a step of 1. Therefore, the NSVD filter actually has the advantages of the SVD filter and smoothing filter. To verify the performance of the NSVD filter, lateral FWHM, CR, CNR, gCNR, and sSNR are assessed in simulation and experiments. Our results indicate that the NSVD filter has little effect on the lateral resolution. However, it does help to reduce noise and can improve the quality of speckle pattern of images beamformed using adaptive weighting methods. Compared to CPWC and CPWC+SVD, CPWC+NSVD can obtain higher CR and CNR. By combining with the NSVD filter, CF, GCF, and SLSC all provide improved CR, CNR, gCNR, and sSNR. The SVD filter can reduce sidelobes and maintain mainlobes due to the high coherence of mainlobe signals and the high incoherence of sidelobe signals, while the number of eigenvalues, \(\beta\), will affect the performance of the SVD filter. As per Figure 4b-c, a smaller \(\beta\) leads to lower sidelobes but a wider mainlobe, which is the same as with the NSVD filter. Therefore, the NSVD filter can hardly reduce the mainlobe width, and thus produces no improvement in the lateral resolution. From both simulated and experimental data, NSVD-based methods achieve a better image contrast than those methods without the use of NSVD, since noises within cysts are further suppressed, as shown in Figures 6, 12 and 15. It can be seen from the B-mode images that adaptive weighting methods influence the speckle pattern. Images of CF, GCF, and SLSC show visible dark-region artifacts and low CNR and sSNR compared to the CPWC image. Multiple studies have indicated that adaptive beamforming methods alter the statistical distribution of the speckle and increase the variance of the background speckle pattern [27; 42], which can be reflected from the degraded sSNR. However, using the NSVD filter in adaptive weighting methods, we can observe decreased dark-region artifacts and background variance in B-mode images, since the NSVD filter has the characteristic of smoothing images. It is also demonstrated that CF+NSVD, GCF+NSVD, and SLSC+NSVD provide higher CNR and sSNR than the corresponding CF, GCF, and SLSC (Figures 7, 13 and 15). From all B-mode images, we see that SLSC+NSVD (\(\beta=3\)) suffers from few artifacts and provides outstanding performance in terms of CR, CNR, gCNR, and sSNR. Therefore, among the methods of CF+NSVD, GCF+NSVD, and SLSC+NSVD, we recommend SLSC+NSVD with \(\beta=3\) as the best overall method. The width of the sliding window (i.e., the size of the neighbor region) and \(\beta\) both have an influence on the imaging performances of the proposed methods. From Figure 17, NSVD-based methods achieve stable CR, CNR, gCNR, and sSNR when the width of the sliding window is larger than 1.6 mm. It should be noted that a wide window for NSVD will increase the computational load. As mentioned, NSVD tends to utilize the neighbor region clues, thus it may not be reasonable to select a large sliding window. From the simulation and experimental results, NSVD with both \(\beta=2\) and \(\beta=3\) can improve the image quality in CR, CNR, gCNR, and sSNR.