After 100 years of theoretical treatment of speckle patterns from coherent illumination, there remain some open questions about the nature of ultrasound speckle from soft vascularized tissues. A recent hypothesis is that the fractal branching vasculature is responsible for the dominant echo pattern from organs such as the liver. In that case, an analysis of cylindrical scattering structures arranged across a power law distribution of sizes is warranted. Using a simple model of echo strength and basic transformation rules from probability, we derive the first order statistics of speckle considering the amplitude, the intensity, and the natural log of amplitude. The results are given by long tailed distributions that have been studied in the statistics literature for other fields. Examples are given from simulations and animal studies, and the theoretical fit to these preliminary data support the overall framework as a plausible model for characterizing ultrasound speckle statistics.

中文翻译：

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来自超声散斑的毛刺、Lomax、Pareto 和 Logistic 分布

在对来自相干照明的散斑图案进行了 100 年的理论处理后，关于来自软血管化组织的超声散斑的性质仍然存在一些悬而未决的问题。最近的一个假设是分形分支脉管系统负责来自器官（如肝脏）的主要回声模式。在这种情况下，有必要对跨尺寸幂律分布排列的圆柱形散射结构进行分析。使用简单的回波强度模型和概率的基本变换规则，我们推导出散斑的一阶统计量，考虑幅度、强度和幅度的自然对数。结果由其他领域的统计文献中研究过的长尾分布给出。例子来自模拟和动物研究，