Céspedes I, Huang Y, Ophir J, Spratt S
University of Texas Medical School Radiology Department, Ultrasonics Laboratory, Houston 77030, USA.
Ultrason Imaging. 1995 Apr;17(2):142-71. doi: 10.1177/016173469501700204.
Time delay estimation (TDE) is commonly performed in practice by crosscorrelation of digitized echo signals. Since time delays are generally not integral multiples of the sampling period, the location of the largest sample of the crosscorrelation function (ccf) is an inexact estimator of the location of the peak. Therefore, one must interpolate between the samples of the ccf to improve the estimation precision. Using theory and simulations, we review and compare the performance of several methods for interpolation of the ccf. The maximum likelihood approach to interpolation is the application of a reconstruction filter to the discrete ccf. However, this method can only be approximated in practice and can be computationally intensive. For these reasons, a simple method is widely used that involves fitting a parabola (or other curve) to samples of the ccf in the neighborhood of its peak. We describe and compare two curve-fitting methods: parabolic and cosine interpolation. Curve-fitting interpolation can yield biased time-delay estimates, which may preclude the use of these methods in some applications. The artifactual effect of these bias errors on elasticity imaging by elastography is discussed. We demonstrate that reconstructive interpolation is unbiased. An iterative implementation of the reconstruction procedure is proposed that can reduce the computation time significantly.
在实际操作中，时延估计（TDE）通常通过对数字化回波信号进行互相关来实现。由于时延一般不是采样周期的整数倍，互相关函数（ccf）最大样本的位置是峰值位置的不精确估计器。因此，必须在ccf的样本之间进行插值以提高估计精度。通过理论和仿真，我们回顾并比较了几种ccf插值方法的性能。插值的最大似然方法是将重建滤波器应用于离散ccf。然而，该方法在实际中只能近似实现，并且计算量可能很大。由于这些原因，一种简单的方法被广泛使用，该方法涉及在ccf峰值附近对其样本拟合一条抛物线（或其他曲线）。我们描述并比较了两种曲线拟合方法：抛物线插值和余弦插值。曲线拟合插值可能会产生有偏差的时延估计，这可能会在某些应用中排除这些方法的使用。讨论了这些偏差误差在弹性成像中对弹性成像的伪影效应。我们证明重建插值是无偏差的。提出了一种重建过程的迭代实现方法，该方法可以显著减少计算时间。
