# Systematic Evaluation on Speckle Suppression Methods in Examination of Ultrasound Breast Images
## 3 Evaluation Criteria Analysis for De-Speckling Performance
### Description of Experiments  
To illustrate the characteristics of the filters and their de-speckling performance, five experiments are performed. In Experiment 1, we explored the relationship between \(\sigma_{d}\) and \(\sigma_{r}\), verified the correctness of the Equation (11), and obtained their detailed relationship curve which can result in the optimal parameters setting. The parameters for the filter are very important. In this experiment, applying the BF to filter the BUS images and tuning the value of \(\sigma_{d}\), we aim to confirm the relationship between \(\sigma_{d}\) and \(\sigma_{r}\) similar to Equation (11) and obtain optimal \(\sigma_{d}\) and \(\sigma_{r}\) for further improvement of the BF. In Experiment 2, by using the experiment of comparing each of PDE methods based on visual, we distinguished the performances from different PDE methods and verified that the diffusion information would affect the de-speckling effect. With drawing the relationship between \(\varphi\) and the VMR in PM diffusion, Equation (33) can be validated. Meanwhile, appropriate \(\varphi\) with appropriate number of iterative runs \(n\) could be obtained for the PDE methods. In this experiment, the PMD and  
Figure 1: The computation for the averaged radical error. Figure 2: The segmentation result: (**a**) original ultrasound image; and (**b**) segmentation result using fuzzy C means method. WJD are compared with each other to find the different performance between isotropic and anisotropic diffusion algorithms based on visual measurement. As typical anisotropic diffusion, the WJD can be regarded as the modified model of PMD which is typical isotropic. In Experiment 3, we conducted the following experiments. First, we selected the edges and homogeneous regions of a specific image, and then adjust the parameters of the filters, respectively, according to the visual measurement (i.e., VMR and LRD). After that, under the radiologists' guidance, we set the parameters for each filter empirically by a number of repeated experiments. We then applied filters to the BUS images, and compute the VMR and LRD value in the homogeneous and edge region of filtered images, respectively. Additionally, comparison was taken according to VMR and LRD to analyze the performance of filters. It should be highlighted that the LRD is extremely sensitive to noise, and the LRD value makes no sense if the image is not de-noised first. To compare two filtered images, the LRD can be carried out in the case of the same VMR of two images. In Experiment 4, the FCM algorithm [51] was utilized for BUS segmentation on the filtered images which have been filtered in Experiment 3. The ARE value can be computed so as to compare image segmentation accuracy. In this experiment, the \"true\" tumor regions of the ultrasound images are manually defined as the average value calculated by three radiologists. The segmentation accuracy evaluation based on the ARE for all filters investigated in this paper was calculated, and their performance were compared. In Experiment 5, we calculated the running time of the filtering algorithms for comparison of the complexity of filtering algorithms. In this experiment, we counted completion time of eight filtering algorithms and compared their complexities. In Experiments 3, 4, and 5, all the eight de-speckling filters adopted in this study were investigated, including WTF, GLF, WF, LF, BF, PMD, WJD, and TV. They were applied to a total of 40 ultrasound images with breast tumors (20 are benign and the rest are malignant). In all five experiments, the BUS images were provided by the Cancer Center of Sun Yat-sen University (Guangzhou, China), and taken from a SonoCT (PhilipsHDI 5000 SonoCT, ATL Philips, Eindhoven, The Netherlands) with a L12-5 50 mm Broadband Linear Array at the imaging frequency of 7.1 MHz. Each image is of 400 \(\times\) 300 pixels in size.