# Systematic Evaluation on Speckle Suppression Methods in Examination of Ultrasound Breast Images
## 5 Discussion  
From the results, it can be seen that in relation to the visual measurement perspective, a smaller variance is required from the homogeneous area of the filtering image so as to achieve a better outcome of removing the additive noise. The WTF's de-noising capability is determined by the threshold value in the wavelet domain, i.e., when the additive noise is seen as WGN, the maximum value of wavelet coefficient of noise decreases as the decomposition scale goes up. Hence, in order to get rid of the additive noise, large wavelet coefficient can be restrained in a bigger decomposition scale. \begin{table}
\begin{tabular}{c c} \hline
**Algorithm** & **ARE (\%)** \\ \hline WTF & 9.20 \(\pm\) 1.80 \\ GLF & 9.69 \(\pm\) 1.55 \\ WF & 9.87 \(\pm\) 1.88 \\ LF & 9.13 \(\pm\) 1.91 \\ BF & 9.10 \(\pm\) 1.51 \\ PMD & 9.74 \(\pm\) 1.92 \\ WJD & 9.60 \(\pm\) 1.75 \\ TV & 9.56 \(\pm\) 1.87 \\ \hline \end{tabular}
\end{table} 
Table 6: The results of averaged radical error (ARE) value for the filters. \begin{table}
\begin{tabular}{c c} \hline
**Algorithm** & **Time (s)** \\ \hline WTF & 3.89 \(\pm\) 0.03 \\ GLF & 3.85 \(\pm\) 0.05 \\ WF & 3.81 \(\pm\) 0.04 \\ LF & 6.51 \(\pm\) 0.03 \\ BF & 6.91 \(\pm\) 0.02 \\ PMD & 2.86 \(\pm\) 0.03 \\ WJD & 11.25 \(\pm\) 0.06 \\ TV & 9.50 \(\pm\) 0.08 \\ \hline \end{tabular}
\end{table} 
Table 7: The completion time of the investigated filters. Similarly, the GLF restrains the additive noise by controlling the high frequency area. However, the edge information of an image, namely severely mutated information, mainly concentrates upon the high decomposition scale in the wavelet domain and lies in the high frequency area of the frequency domain. In the application of WTF, the decomposition scale which contains most energy of noise is difficult to determine. For the GLF, position of noise in spectrum is also hard to determine. Therefore, in relation to the preservation and reinforcement of edge, effective method is the missing link in specifically determining whether to restrain or resolve the scale and high frequency position. The WF is widely used as an MMSE filter. However, the WF's drawbacks are obvious, i.e., its capability of suppressing the additive noise is determined by the estimation of \(S_{f}(u,v)/S_{g}(u,v)\) and \(H(u,v)\). Equation (13) is determined by channel estimation, but both of the former estimations cannot be accurately obtained on account of the features of medical ultrasound images. Therefore, under the circumstance where theoretical instruction is lacking, preferable capability cannot be achieved even through repeated experiments. Generally, the MMSE filter is a linear filter such that it blurs the image when reducing speckle noises [20]. Furthermore, it has been known that linear filters do not perform well in de-speckling since it blurs sharp edges [21; 56]. As for the LF, its capability of de-noising for additive noise is determined by the variance of the additive noise. In addition, its ability of reversing degradation mainly depends on the variance of the multiplicative noise. Nevertheless, with regard to the medical ultrasound image, the following problems appear: (1) probability distribution function of \(n_{m}\) cannot be accurately estimated; (2) during the approximated evaluation of probability density function, SNR of different imaging regions are uncertain, variance of \(n_{m}\) cannot be accurately derived, and \(\sigma_{2}\) remains unknown; and (3) the inevitable error existing in the estimation of variance of \(n_{a}\) brings major negative impact. In order to make the problems simplified, in the experiment, we gained a better ability in reversing degradation by assuming that the PDF of multiplicative noise follows Gaussian distribution \(N\) (1, 0.02). On the other hand, we can easily figure it out that, theoretically, suppression of additive noise can be reached in the area where variance of \(n_{a}\) can be accurately estimated or the degree of degradation is weak.