IEEE Trans Ultrason Ferroelectr Freq Control. 2017 Apr;64(4):669-678. doi: 10.1109/TUFFC.2017.2652451. Epub 2017 Jan 16.
Despite a great deal of work characterizing the statistical properties of radio frequency backscattered ultrasound signals, less is known about the statistical properties of demodulated intensity signals. Analysis of intensity is made more difficult by a strong nonlinearity that arises in the process of demodulation. This limits our ability to characterize the spatial resolution and noise properties of B-mode ultrasound images. In this paper, we generalize earlier results on two-point intensity covariance using a multivariate systems approach. We derive the mean and autocovariance function of the intensity signal under Gaussian assumptions on both the object scattering function and acquisition noise, and with the assumption of a locally shift-invariant pulse-echo system function. We investigate the limiting cases of point statistics and a uniform scattering field with a stationary distribution. Results from validation studies using simulation and data from a real system applied to a uniform scattering phantom are presented. In the simulation studies, we find errors less than 10% between the theoretical mean and variance, and sample estimates of these quantities. Prediction of the intensity power spectrum (PS) in the real system exhibits good qualitative agreement (errors less than 3.5 dB for frequencies between 0.1 and 10 cyc/mm, but with somewhat higher error outside this range that may be due to the use of a window in the PS estimation procedure). We also replicate the common finding that the intensity mean is equal to its standard deviation (i.e., signal-to-noise ratio = 1) for fully developed speckle. We show how the derived statistical properties can be used to characterize the quality of an ultrasound linear array for low-contrast patterns using generalized noise-equivalent quanta directly on the intensity signal.
尽管已经有大量的工作对射频反向散射超声信号的统计特性进行了描述，但对解调强度信号的统计特性却知之甚少。解调过程中出现的强非线性使得对强度的分析变得更加困难。这限制了我们对 B 模式超声图像的空间分辨率和噪声特性进行特征描述的能力。在本文中，我们使用多变量系统方法对两点强度协方差的早期结果进行了推广。我们推导了在对象散射函数和采集噪声的高斯假设下，以及在局部平移不变脉冲回波系统函数的假设下，强度信号的均值和自协方差函数。我们研究了点统计和具有平稳分布的均匀散射场的极限情况。使用模拟和应用于均匀散射体的真实系统的数据进行验证研究的结果。在模拟研究中，我们发现理论均值和方差与这些量的样本估计值之间的误差小于 10%。在真实系统中，对强度功率谱 (PS) 的预测显示出良好的定性一致性（在 0.1 到 10 个 cyc/mm 之间的频率下，误差小于 3.5 dB，但在该范围之外，误差可能稍高，这可能是由于在 PS 估计过程中使用了窗口）。我们还复制了常见的发现，即完全发展的散斑的强度均值与其标准差相等（即信噪比=1）。我们展示了如何使用推导的统计特性直接在强度信号上使用广义噪声等效量子来描述用于低对比度模式的超声线阵的质量。
