Fast computation of far-field pulse-echo PSF of arbitrary arrays for large sparse 2-D ultrasound array design

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.