## 1 Introduction  
Ultrasound images (UI) are becoming more and more popular in clinical diagnosis due to their economical and practical advantages. However, due to the eliminative or constructive interference between different ultrasonic waves during the image generation phase, the collected UIs inevitably contain speckle-patterned noise. Affected by the speckle noise, UIs always exhibit low resolution, which raises the difficulty of identification and diagnosis in clinical practice. Furthermore, the accuracy of many tasks designed to assist diagnosis, such as image segmentation [1] or detection and classification [2], will also be degraded by the speckle noise. How to reduce the noise effects while effectively preserving the image details is becoming a challenging problem. Many methods have been proposed to solve this problem, and most de-noising methods try to infer the true images based on the information redundancy character of the noisy images. For example, transform domain methods are mainly based on the assumption that an image can be sparsely represented by basic components, and so the noise is uniformly spread throughout the coefficients in the transform domain [3]. The useful details are concentrated in the largest parts of the high frequency components, while the noise exists in smaller ones; so, we can use some shrinking strategies to remove or reduce the noise. However, these kinds of methods face the risk of introducing pseudo-Gibbs artifacts when using a hard-shrinking strategy, or of over-smoothing when using a soft-shrinking strategy. As an interesting solution, [PERSON] et al. proposed a data-driven method to adapt the wavelet threshold paradigm [4]. An extensive review of despeckling methods using various transformation techniques can be found in [5]. Along another line, the commonly used spatial domain methods [6; 7; 8; 9] use local statistics to represent the information of the recovered images. These methods are often based on the multiplicative speckle model. The most successful methods among them are anisotropic diffusion [9] and the bilateral filter [6], which are all well-known due to their good ability for preserving edges. However, these kinds of methods corrupt the correlations between neighboring pixels, and thus perform badly for images with strong noise [3; 10]. Inspired by the idea of decreasing pixel variation in homogenous regions while maintaining (or improving) the differences in the mean values of different regions, [PERSON] et al. developed a squeeze box filter (SBF) to remove speckle noise [11]. Moreover, another group of sparse representation methods--namely non-local methods--has been proposed, in order to break the local dependence. In general, these methods use the property of information redundancy among similar patches to reduce the noise [12; 13]. The common difficulty in these kinds of methods is how to find the candidate patches, as unsuitable candidate patches greatly reduce the de-noising performance, especially for the ultrasound images with strong noise. Recently, [PERSON] et al. [14] used a guidance image, derived from the windowed inherent variation measure [15], to overcome this problem. Furthermore, [PERSON] et al. combined local and non-local properties and used the local statistics to help the selection of similar patches [16]. [PERSON] et al. developed a modified version of the efficient block-matching collaborative filtering (BM3D) de-speckling method, based on the well-known statistical divergences [17]. Recently, [PERSON] et al. proposed a multiplicative speckle suppression technique, based on sparse representation over dictionary learning [18]. Non-local methods always use a square window to search for similar patches. However, this strategy is not always suitable for edge regions. Additionally, the patch size needs to be pre-learned and then fixed for the test images. Based on the superpixel properties around the region edges, [PERSON] et al. [19] proposed a method of superpixel-guided non-local means for natural image noise reduction.