Tuvi Ram
John A. and Katherine G. Jackson School of Geosciences, Institute for Geophysics, The University of Texas at Austin, Austin, TX 78758, USA.
Sensors (Basel). 2022 Feb 21;22(4):1684. doi: 10.3390/s22041684.
We present an overview of a beam-based approach to ultra-wide band (UWB) tomographic inverse scattering, where beam-waves are used for local data-processing and local imaging, as an alternative to the conventional plane-wave and Green's function approaches. Specifically, the method utilizes a phase-space set of iso-diffracting beam-waves that emerge from a discrete set of points and directions in the source domain. It is shown that with a proper choice of parameters, this set constitutes (an overcomplete generalization of a basis), termed "beam frame", over the entire propagation domain. An important feature of these beam frames is that they need to be calculated once and then used for all frequencies, hence the method can be implemented either in the multi-frequency domain (FD), or directly in the time domain (TD). The algorithm consists of two phases: in the processing phase, the scattering data is transformed to the beam domain using windowed phase-space transformations, while in the imaging phase, the beams are backpropagated to the target domain to form the image. The beam-domain data is not only localized and compressed, but it is also physically related to the local Radon transform (RT) of the scatterer via a local Snell's reflection of the beam-waves. This expresses the imaging as an inverse local RT that can be applied to any local domain of interest (DoI). In previous publications, the emphasis has been set on TD data processing using a special class of localized space-time beam-waves (wave-packets). The goal of the present paper is to present the imaging scheme in the UWB FD, utilizing simpler Fourier-based data-processing tools in the space and time domains.
我们概述了一种基于波束的超宽带（UWB）层析成像逆散射方法，该方法使用波束波进行局部数据处理和局部成像，作为传统平面波和格林函数方法的替代方案。具体而言，该方法利用了一组等衍射波束波的相空间集，这些波束波从源域中的一组离散点和方向发出。结果表明，通过适当选择参数，该集合在整个传播域上构成（一种基的超完备推广），称为“波束框架”。这些波束框架的一个重要特征是，它们只需计算一次，然后用于所有频率，因此该方法可以在多频域（FD）中实现，也可以直接在时域（TD）中实现。该算法由两个阶段组成：在处理阶段，使用加窗相空间变换将散射数据转换到波束域，而在成像阶段，将波束反向传播到目标域以形成图像。波束域数据不仅是局部化和压缩的，而且通过波束波的局部斯涅尔反射与散射体的局部拉东变换（RT）存在物理关联。这将成像表示为一种逆局部RT，可应用于任何感兴趣的局部域（DoI）。在以前的出版物中，重点一直放在使用一类特殊的局部时空波束波（波包）进行TD数据处理上。本文的目标是在UWB FD中提出成像方案，在空间和时域中使用更简单的基于傅里叶的数据处理工具。
