Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA 22904, USA.
IEEE Trans Image Process. 2002;11(11):1260-70. doi: 10.1109/TIP.2002.804276.
This paper provides the derivation of speckle reducing anisotropic diffusion (SRAD), a diffusion method tailored to ultrasonic and radar imaging applications. SRAD is the edge-sensitive diffusion for speckled images, in the same way that conventional anisotropic diffusion is the edge-sensitive diffusion for images corrupted with additive noise. We first show that the Lee and Frost filters can be cast as partial differential equations, and then we derive SRAD by allowing edge-sensitive anisotropic diffusion within this context. Just as the Lee and Frost filters utilize the coefficient of variation in adaptive filtering, SRAD exploits the instantaneous coefficient of variation, which is shown to be a function of the local gradient magnitude and Laplacian operators. We validate the new algorithm using both synthetic and real linear scan ultrasonic imagery of the carotid artery. We also demonstrate the algorithm performance with real SAR data. The performance measures obtained by means of computer simulation of carotid artery images are compared with three existing speckle reduction schemes. In the presence of speckle noise, speckle reducing anisotropic diffusion excels over the traditional speckle removal filters and over the conventional anisotropic diffusion method in terms of mean preservation, variance reduction, and edge localization.
本文提供了斑点减少各向异性扩散（SRAD）的推导，这是一种针对超声和雷达成像应用量身定制的扩散方法。SRAD 是针对具有斑点的图像的边缘敏感扩散，就像常规各向异性扩散是针对具有加性噪声的图像的边缘敏感扩散一样。我们首先证明 Lee 和 Frost 滤波器可以表示为偏微分方程，然后通过在这种情况下允许边缘敏感各向异性扩散来推导出 SRAD。就像 Lee 和 Frost 滤波器在自适应滤波中利用变差系数一样，SRAD 利用瞬时变差系数，该系数被证明是局部梯度幅度和拉普拉斯算子的函数。我们使用颈动脉的合成和真实线性扫描超声图像来验证新算法。我们还使用真实 SAR 数据展示了该算法的性能。通过对颈动脉图像进行计算机模拟获得的性能指标与三种现有的斑点减少方案进行了比较。在存在斑点噪声的情况下，与传统的斑点去除滤波器和常规的各向异性扩散方法相比，斑点减少各向异性扩散在均值保持、方差减少和边缘定位方面表现出色。
