In ultrasound nondestructive testing (NDT), a widespread approach is to take synthetic aperture measurements from the surface of a specimen to detect and locate defects within it. Based on these measurements, imaging is usually performed using the synthetic aperture focusing technique (SAFT). However, SAFT is suboptimal in terms of resolution and requires oversampling in the time domain to obtain a fine grid for the delay-and-sum (DAS). On the other hand, parametric reconstruction algorithms give better resolution, but their usage for imaging becomes computationally expensive due to the size of the parameter space and a large amount of measurement data in realistic 3-D scenarios when using oversampling. In the literature, the remedies to this are twofold. First, the amount of measurement data can be reduced using state-of-the-art sub-Nyquist sampling approaches to measure Fourier coefficients instead of time-domain samples. Second, parametric reconstruction algorithms mostly rely on matrix-vector operations that can be implemented efficiently by exploiting the underlying structure of the model. In this article, we propose and compare different strategies to choose the Fourier coefficients to be measured. Their asymptotic performance is compared by numerically evaluating the Cramér-Rao bound (CRB) for the localizability of the defect coordinates. These subsampling strategies are then combined with an l1 -minimization scheme to compute 3-D reconstructions from the low-rate measurements. Compared to conventional DAS, this allows us to formulate a fully physically motivated forward model matrix. To enable this, the projection operations of the forward model matrix are implemented matrix-free by exploiting the underlying two-level Toeplitz structure. Finally, we show that high-resolution reconstructions from as low as a single Fourier coefficient per A-scan are possible based on simulated data and measurements from a steel specimen.

中文翻译：

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超声无损测量的频率二次采样：采集、重建和性能。

在超声无损检测 (NDT) 中，一种广泛使用的方法是从样品表面进行合成孔径测量，以检测和定位其中的缺陷。基于这些测量，通常使用合成孔径聚焦技术 (SAFT) 进行成像。然而，SAFT 在分辨率方面是次优的，需要在时域中进行过采样以获得延迟求和 (DAS) 的精细网格。另一方面，参数重建算法提供更好的分辨率，但由于参数空间的大小和使用过采样时在现实 3-D 场景中的大量测量数据，它们用于成像的计算成本很高。在文献中，对此的补救措施是双重的。第一的，使用最先进的亚奈奎斯特采样方法来测量傅立叶系数而不是时域采样，可以减少测量数据的数量。其次，参数重建算法主要依赖于矩阵向量运算，这些运算可以通过利用模型的底层结构来有效实现。在本文中，我们提出并比较了选择要测量的傅立叶系数的不同策略。它们的渐近性能通过数值评估 Cramér-Rao 界 (CRB) 的缺陷坐标可定位性来比较。然后将这些子采样策略与 l1 最小化方案相结合，以根据低速率测量计算 3-D 重建。与传统的 DAS 相比，这使我们能够制定一个完全由物理驱动的前向模型矩阵。为了实现这一点，前向模型矩阵的投影操作通过利用底层的两级 Toeplitz 结构实现无矩阵。最后，我们表明，基于钢试样的模拟数据和测量值，可以从每个 A 扫描的单个傅立叶系数进行高分辨率重建。