2020/12/08 by Jan Kirchhof, Kirchhof, Jan, Sebastian Semper +9
Engineering · #FOS: Electrical engineering #Non-Destructive Testing Techniques #Signal Processing (eess.SP) #Structural Health Monitoring Techniques #Ultrasonics and Acoustic Wave Propagation #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2012.04534
openalex publication_date 2020/12/08 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
In ultrasound nondestructive testing, a widespread approach is to take\nsynthetic aperture measurements from the surface of a specimen to detect and\nlocate defects within it. Based on these measurements, imaging is usually\nperformed using the Synthetic Aperture Focusing Technique (SAFT). However, SAFT\nis sub-optimal in terms of resolution and requires oversampling in time domain\nto obtain a fine grid for the Delay-and-Sum (DAS). On the other hand,\nparametric reconstruction algorithms give better resolution, but their usage\nfor imaging becomes computationally expensive due to the size of the parameter\nspace and the large amount of measurement data in realistic 3-D scenarios. In\nthe literature, the remedies to this are twofold: First, the amount of\nmeasurement data can be reduced using state of the art sub-Nyquist sampling\napproaches to measure Fourier coefficients instead of time domain samples.\nSecond, parametric reconstruction algorithms mostly rely on matrix-vector\noperations that can be implemented efficiently by exploiting the underlying\nmodel structure. In this paper, we propose and compare different strategies to\nchoose the Fourier coefficients to be measured. Their asymptotic performance is\ncompared by numerically evaluating the Cram 'er-Rao-Bound for the\nlocalizability of the defect coordinates. These subsampling strategies are then\ncombined with an \ℓ1-minimization scheme to compute 3-D reconstructions\nfrom the low-rate measurements. Compared to conventional DAS, this allows us to\nformulate a fully physically motivated forward model. To enable this, the\nprojection operations of the forward model matrix are implemented matrix-free\nby exploiting the underlying 2-level Toeplitz structure. Finally, we show that\nhigh resolution reconstructions from as low as a single Fourier coefficient per\nscan are possible based on simulated data as well as on measurements.\n