Xu Kailiang, Laugier Pascal, Minonzio Jean-Gabriel
Sorbonne Universités, UPMC Univ Paris 06, CNRS, INSERM, Laboratoire d'Imagerie Biomédicale (LIB), 15 rue de l'école de médecine, 75006, Paris, France.
J Acoust Soc Am. 2018 May;143(5):2729. doi: 10.1121/1.5036726.
Dispersion results in the spreading and overlapping of the wave-packets, which often limits the capability of signal interpretation; on the other hand, such a phenomenon can also be used for structure or media evaluation. In this study, the authors propose an original dispersive Radon transform (DRT), which is formulated as integration transform along a set of dispersion curves. Multichannel dispersive signals of each individual mode can be concentrated to a well localized region in the DRT domain. The proposed DRT establishes the sparse projection of the dispersive components and provides an efficient solution for mode separation, noise filtering, and missing data reconstruction. Particularly the DRT method allows projecting the temporal signals of dispersive waves on the space of parameters of interest, which can be used to solve the inverse problem for waveguide or media property estimation. The least-square procedure and sparse scheme of the DRT are introduced. A high-resolution DRT is designed based on an iterative reweighting inversion scheme, which resembles the infinite-aperture velocity gather. The proposed method is applied by analyzing ultrasonic guided waves in plate-like structures and in a human radius specimen. The results suggest that the DRT method can significantly enhance the interpretation of dispersive signals.
频散会导致波包的扩展和重叠，这常常限制信号解读的能力；另一方面，这种现象也可用于结构或介质评估。在本研究中，作者提出了一种原创的频散拉东变换（DRT），它被定义为沿一组频散曲线的积分变换。每个单独模式的多通道频散信号可以在DRT域中被集中到一个定位良好的区域。所提出的DRT建立了频散分量的稀疏投影，并为模式分离、噪声滤波和缺失数据重建提供了一种有效的解决方案。特别是，DRT方法允许将频散波的时间信号投影到感兴趣的参数空间上，这可用于解决波导或介质特性估计的反问题。介绍了DRT的最小二乘法和稀疏方案。基于一种类似于无限孔径速度道集的迭代重加权反演方案设计了一种高分辨率DRT。通过分析板状结构和人体桡骨标本中的超声导波来应用所提出的方法。结果表明，DRT方法可以显著增强对频散信号的解读。
