In the context of nondestructive testing (NDT), this article proposes an inverse problem approach for the reconstruction of high-resolution ultrasonic images from full matrix capture (FMC) data sets. We build a linear model that links the FMC data, i.e., the signals collected from all transmitter–receiver pairs of an ultrasonic array, to the discretized reflectivity map of the inspected object. In particular, this model includes the ultrasonic waveform corresponding to the response of transducers. Despite a large amount of data, the inversion problem is ill-posed. Therefore, a regularization strategy is proposed, where the reconstructed image is defined as the minimizer of a penalized least-squares cost function. A mixed penalization function is considered, which simultaneously enhances the sparsity of the image (in NDT, the reflectivity map is mostly zero except at the flaw locations) and its spatial smoothness (flaws may have some spatial extension). The proposed method is shown to outperform two well-known imaging methods: the total focusing method (TFM) and Excitelet. Numerical simulations with two close reflectors show that the proposed method improves the resolution limit defined by the Rayleigh criterion by a factor of four. Such high-resolution imaging capability is confirmed by experimental results obtained with side-drilled holes in an aluminum sample.

中文翻译：

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从完整矩阵捕获数据进行超声成像的逆方法：在无损检测中提高分辨率的应用

在无损检测（NDT）的背景下，本文提出了一种从全矩阵捕获（FMC）数据集中重建高分辨率超声图像的逆问题方法。我们建立了一个线性模型，该模型将FMC数据（即从超声波阵列的所有发射器-接收器对中收集的信号）链接到被检查对象的离散反射率图。特别地，该模型包括与换能器的响应相对应的超声波形。尽管有大量数据，但反演问题仍然存在。因此，提出了一种正则化策略，其中将重建图像定义为惩罚最小二乘成本函数的最小化器。考虑了混合惩罚功能，可同时增强图像的稀疏度（在NDT中，反射率贴图除在缺陷位置以外大部分为零）及其空间平滑度（缺陷可能具有一定的空间扩展）。结果表明，所提出的方法优于两种众所周知的成像方法：全聚焦方法（TFM）和Excitelet。使用两个紧密反射器的数值模拟表明，该方法将瑞利准则定义的分辨率极限提高了四倍。通过在铝样品中钻孔的实验结果证实了这种高分辨率的成像能力。使用两个紧密反射器的数值模拟表明，该方法将瑞利准则定义的分辨率极限提高了四倍。通过在铝样品中钻孔的实验结果证实了这种高分辨率的成像能力。使用两个紧密反射器的数值模拟表明，该方法将瑞利准则定义的分辨率极限提高了四倍。通过在铝样品中侧面钻孔获得的实验结果证实了这种高分辨率的成像能力。