IEEE Trans Ultrason Ferroelectr Freq Control. 2019 Dec;66(12):1830-1844. doi: 10.1109/TUFFC.2019.2933506. Epub 2019 Aug 6.
We present a statistical interpretation of beamforming to overcome the limitations of standard delay-and-sum (DAS) processing. Both the interference and the signal of interest are viewed as random variables, and the distribution of the signal of interest is exploited to maximize the a posteriori distribution of the aperture signals. In this formulation, the beamformer output is a maximum a posteriori (MAP) estimator of the signal of interest. We provide a closed-form expression for the MAP beamformer and estimate the unknown distribution parameters from the available aperture data using an empirical Bayes approach. We propose a simple scheme that iterates between the estimation of distribution parameters and the computation of the MAP estimator of the signal of interest, leading to an iterative MAP (iMAP) beamformer. This results in a suppression of the interference compared with DAS, without a severe increase in computational complexity or the need for fine-tuning of parameters. The effect of the proposed method on contrast is studied in detail and measured in terms of contrast ratio (CR), contrast-to-noise ratio (CNR), and contrast-to-speckle ratio (CSR). By implementing iMAP on both simulated and experimental data, we show that only 13 transmissions are required to obtain a CNR comparable to DAS with 75 plane waves. Compared to other interference suppression methods, such as coherence factor and scaled Wiener processing, iMAP shows an improved contrast and a better preserved speckle pattern.
我们提出了一种基于统计的波束形成方法,以克服标准延迟和求和(DAS)处理的局限性。将感兴趣的信号和干扰都视为随机变量,并利用感兴趣的信号分布来最大化孔径信号的后验分布。在这种表述中,波束形成器的输出是感兴趣信号的最大后验(MAP)估计器。我们提供了 MAP 波束形成器的闭式表达式,并使用经验贝叶斯方法从可用孔径数据中估计未知的分布参数。我们提出了一种简单的方案,在分布参数的估计和感兴趣信号的 MAP 估计器的计算之间迭代,从而得到迭代 MAP(iMAP)波束形成器。与 DAS 相比,这会抑制干扰,而不会严重增加计算复杂度或需要微调参数。详细研究了该方法对对比度的影响,并通过对比度比(CR)、对比度噪声比(CNR)和对比度散斑比(CSR)来衡量。通过在模拟和实验数据上实现 iMAP,我们表明只需要 13 次发射即可获得与 75 个平面波相当的 CNR。与其他干扰抑制方法(如相干因子和比例维纳处理)相比,iMAP 显示出更好的对比度和更好的散斑图案保留。