Li Zhaohui, Chi Cheng
Department of Electronics, Peking University, No. 5 Yiheyuan Road, Haidian District, Beijing 100871, China.
Department of Electronics, Peking University, No. 5 Yiheyuan Road, Haidian District, Beijing 100871, China.
Ultrasonics. 2018 Mar;84:63-73. doi: 10.1016/j.ultras.2017.10.006. Epub 2017 Oct 10.
Large wideband two-dimensional (2-D) arrays are essential for high-resolution three-dimensional (3-D) ultrasound imaging. Since the tremendous element number of a full sampled large 2-D array is not affordable in any practical 3-D ultrasound imaging system, it is necessary to reduce the element number through sparse 2-D array design. Sparse array design requires that both the positions and weights of the array elements should be arbitrarily alterable. Hence a proper evaluation tool that can deal with arbitrary array is integral to optimizing the array structure and apodization function. It is known that pulse-echo point spread function (PSF) has been a common tool used to evaluate the performance of wideband arrays in ultrasound imaging all along, which also plays an important role in wideband ultrasound simulations. However, so far the conventional ultrasound simulation tools can only calculate pulse-echo PSF of arbitrary wideband arrays in the time domain because of the existence of nonuniform nodes in the spatial impulse response expressions, which obstructs their application of FFT to do fast computation of the time-domain convolutions. As a result, ultra-high time consumption of pulse-echo PSF computation of a large arbitrary wideband array hampers it to be taken as the evaluation tool by any stochastic optimization methods which need massive iterations in designing large sparse 2-D arrays. This paper aims to make available the pulse-echo PSF tool in designing large sparse 2-D arrays by proposing a fast computation method of far-field pulse-echo PSFs of arbitrary wideband arrays. In the paper, fast computation of wideband spatial impulse responses of a 2-D array is first realized in frequency domain by employing the nonuniform fast Fourier transform (NUFFT), under the point source assumption in far-field. On the basis of that, fast computation of time-domain convolutions is made possible by using FFT. In addition, a short inverse FFT (IFFT) is applied in recovering the time-domain envelopes rather than the detailed waveforms of beam pulses to extract the pulse-echo PSF, which further accelerates the computation. Compared with the computation speed of the time domain method, i.e. Field II, the proposed method achieves an improvement of three orders of magnitude with comparable accuracy for a 100×100 wideband 2-D array. The proposed method makes it possible for applying stochastic optimization methods to design arbitrary large wideband 2-D arrays using pulse-echo PSF as the evaluation tool.
大型宽带二维（2-D）阵列对于高分辨率三维（3-D）超声成像至关重要。由于在任何实际的3-D超声成像系统中，全采样大型2-D阵列所需的巨大元件数量都难以承受，因此有必要通过稀疏二维阵列设计来减少元件数量。稀疏阵列设计要求阵列元件的位置和权重都应可任意改变。因此，一个能够处理任意阵列的合适评估工具对于优化阵列结构和变迹函数是不可或缺的。众所周知，脉冲回波点扩散函数（PSF）一直是用于评估超声成像中宽带阵列性能的常用工具，它在宽带超声模拟中也起着重要作用。然而，到目前为止，由于空间脉冲响应表达式中存在不均匀节点，传统的超声模拟工具只能在时域中计算任意宽带阵列的脉冲回波PSF，这阻碍了它们应用快速傅里叶变换（FFT）来进行时域卷积的快速计算。结果，大型任意宽带阵列的脉冲回波PSF计算的超高时间消耗阻碍了它被用作任何在设计大型稀疏二维阵列时需要大量迭代的随机优化方法的评估工具。本文旨在通过提出一种任意宽带阵列远场脉冲回波PSF的快速计算方法，使脉冲回波PSF工具可用于设计大型稀疏二维阵列。在本文中，首先在远场点源假设下，通过采用非均匀快速傅里叶变换（NUFFT）在频域中实现二维阵列宽带空间脉冲响应的快速计算。在此基础上，利用FFT实现时域卷积的快速计算。此外，应用短逆快速傅里叶变换（IFFT）来恢复时域包络而不是波束脉冲的详细波形以提取脉冲回波PSF，这进一步加快了计算速度。与时域方法（即Field II）的计算速度相比，对于100×100宽带二维阵列，所提出的方法在精度相当的情况下实现了三个数量级的提升。所提出的方法使得使用脉冲回波PSF作为评估工具应用随机优化方法来设计任意大型宽带二维阵列成为可能。
