# Systematic Evaluation on Speckle Suppression Methods in Examination of Ultrasound Breast Images
###### Abstract
However, the noise and the location in an image are not relevant to each other. Therefore, we are unable to locate the noise in the frequency domain, which results in the inability to accurately separate the noise from the image. Currently, speckle reduction via filtering in the wavelet domain has aroused concern, e.g., the idea of soft-thresholding de-noising first presented by [PERSON] [10]. However, two major drawbacks of the thresholding methods should be concerned [11]. Firstly, it is almost impossible to find the optimal solution for all kinds of images. Secondly, it is unadvisable to use the same noise model for the diverse resolutions. Although the wavelet spectrum can present more details than the frequency spectrum, the problem of how to recognize the noise remains unsolved. For the filtering method based on local statistical properties, adaptive mean filters [12; 13] have been proposed. These filters remove speckle noise via local image statistics such as mean and variance, instead of requiring degradation and noise function. In the homogeneous region of the image, filters act like a mean filter, while in the edge region they act like a nearly all-past filter. However, the performance of de-speckling is constrained by the local statistics that are ineffective in some cases, such as the de-speckling area contains both speckle noise and significant texture. Non-local means (NLM) de-noising [14; 15] has been a focus of research in recent years, which is based on the non-local averaging of all pixels in the image. In particular, the weight of each point is proportional to the similarity of its neighborhood with that of the point being filtered. After the non-local means filter was proposed, the concept of non-local was rapidly adopted by other researchers [16; 17]. The Bilateral Filter (BF), as a specialization of NLM filter algorithms, has been more widely applied in de-speckling due to its user-friendliness and less time consumption [18]. For the filtering method based on the MMSE, this type of filtering algorithm already proposed for de-speckling [19] includes the process of additive noise suppression and inverse degradation. The goal is to find the estimated value \(I_{\underset{f}{\sim}}\) of non-contaminated image from \(I_{g}\) by minimizing mean square error between \(I_{g}\) and \(I_{\underset{f}{\sim}}\). In order to obtain \(I_{\underset{f}{\sim}}\), it is necessary to obtain degradation and additive noise function, which is quite difficult because of the characteristic of BUS image. Besides, the MMSE filter is a linear filter and reduces speckle noise with blurring the image [20]. It has been known that linear filters do not perform well in de-speckling since it blurs sharp edges [21], and the sharp edges are very important for segmentation of tumors. The PDE methods applied to achieve high-quality image de-noising have attracted extensive attention [7; 22]. The diffusion filtering category includes isotropic model such as Perona-Malik diffusion (PMD) filter [23], anisotropic model such as Weickert J Diffusion (WJD) filter [24], and another diffusion model such as Total Variation (TV) filter which was first proposed by [PERSON] et al. [25]. In PMD model, the value of diffusion coefficient is only relevant to the magnitude gradient of image. However, according to WJD and TV models, both the value and direction of diffusion are taken into account. Therefore, the PMD model is the simplest one among these three algorithms, but is more sensitive to noise. In the past decades, a large amount of algorithms have been proposed to contribute to medical ultrasound image filtering, and some works have been done to compare their performances. [PERSON] et al. [26] has compared 10 de-speckle filters in ultrasound images of the carotid artery bifurcation based on texture analysis, image quality evaluation metrics, and visual evaluation. [PERSON] et al. [27] described fifteen speckle filters for the application of echocardiography, and it also discussed the computational performance of the filters.