# Systematic Evaluation on Speckle Suppression Methods in Examination of Ultrasound Breast Images
## 5 Discussion
As a simple algorithm, the BF is the Gaussian low pass filter which is able to make VMR ascend by reducing the noise frequency component. It proves its strong ability in eliminating additive noise in the homogeneous area. Moreover, the BF obtains favorable capability in experiments by maintaining edge information. In Equation (6), the weight of a pixel whose Euclidean distance from the central pixel being filtered is larger than \(\sigma_{d}\) can be decreased. On the other hand, the weight of a pixel will decline if its intensity difference with the central pixel which is filtered is greater than \(\sigma_{r}\). As is indicated, it is not difficult to prove that the BF can meet the requirements of visual measurement. Moreover, depending on the results of Experiment 3 in Section 4, two conclusions can be easily drawn: (1) In order to keep the LRD from changing when increasing \(\sigma_{d}\), \(\sigma_{r}\) must be increased simultaneously, and the relationship between \(\sigma_{d}\) and \(\sigma_{r}\) nearly obeys \(\sigma_{d}{}^{2}\propto 1/\sigma_{r}{}^{2}\) in Equation (11); and (2) VMR(1/MR) ascends as the value of \(\sigma_{d}\) goes up, yet for the purpose of keeping LRD from changing, the value of \(\sigma_{d}\) cannot be too high. Generally speaking, when the average value of \(\sigma_{d}\) and \(\sigma_{r}\) reaches more or less than 20, the BF achieves optimal outcome. For these three filtering algorithms based on PDF, the PMD model is considered as an isotropic diffusion model for it does not consider the direction of gradient of image during the diffusion processing. The WJD and TV can be regarded as anisotropic diffusion models for they consider the diffusion direction during diffusion processing. Among these models, the PMD is the simplest one. However, compared with WJD and TV, the PMD model is more sensitive to noise and can obtain less continuous edge for the reason that it takes diffused strength into account instead of the direction. Therefore, although the PMD can get higher LRD in the case of high VMR, it does not achieve a good effect in image segmentation. With respect to the results of Experiment 2, we can promote to two conclusions:  
(1) More continuous edge obtained in anisotropic diffusion: If some part of the original edge is blurred, the diffusion at discontinuous points becomes stagnant in isotropic diffusion. However,in anisotropic diffusion, the diffusion vertical to edge direction becomes weaker while parallel to edge direction keeps going on, which results in a more continuous edge. 2. Isotropic diffusion is more sensitive to noise: In isotropic diffusion, the diffusion function \(\varphi\) is only relevant to \(\left|\
abla I_{g}(t)\right|\) (i.e., \(\left|\varphi\right|\propto 1/\left|\
abla I_{g}(t)\right|\)).However, in anisotropic diffusion, one diffusion function is vertical to edge (i.e., \(\left|\varphi_{vertical}\right|\propto 1/\left|\
abla I_{g}(t)\right|\)), and another diffusion function is parallel to edge (i.e., \(\left|\varphi_{parallel}\right|\propto\left|\
abla I_{g}(t)\right|\)). Therefore, in isotropic diffusion, noise exists in the homogeneous region causes discontinuous diffusion; but in anisotropic diffusion, the noise is likely to become weakened because the diffusion is vertical to edge direction. At the same time, in Table 3, the result following Equation (34) is that the greater \(\varphi\) enhances the negative impact of noise. That is to say, we should set \(\varphi\) appropriately to reach the balance between iterative time and noise-sensitiveness. Most of the abbreviations used in this paper are described in Table 11.