Inverse scattering is the process of estimating the spatial distribution of the scattering potential of an object by measuring the scattered wavefields around it. In this article, we consider reflection tomography of high contrast objects that commonly occurs in ground-penetrating radar, exploration geophysics, terahertz imaging, ultrasound, and electron microscopy. Unlike conventional transmission tomography, the reflection regime is severely ill-posed since the measured wavefields contain far less spatial frequency information of the target object. We propose a constrained incremental frequency inversion framework that requires no side information from a background model of the object. Our framework solves a sequence of regularized least-squares subproblems that ensure consistency with the measured scattered wavefield while imposing total-variation and non-negativity constraints. We propose a proximal Quasi-Newton method to solve the resulting subproblem and devise an automatic parameter selection routine to determine the constraint of each subproblem. We validate the performance of our approach on synthetic low-resolution phantoms and with a mismatched forward model test on a high-resolution phantom.

中文翻译：

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具有全变约束的高对比度反射层析成像

逆散射是通过测量物体周围的散射波场来估​​计物体散射势空间分布的过程。在本文中，我们考虑了通常出现在探地雷达、勘探地球物理学、太赫兹成像、超声和电子显微镜中的高对比度物体的反射断层扫描。与传统的透射断层扫描不同，反射机制是严重不适定的，因为测量的波场包含的目标物体的空间频率信息要少得多。我们提出了一种约束增量频率反演框架，它不需要来自对象背景模型的辅助信息。我们的框架解决了一系列正则化的最小二乘子问题，确保与测量的散射波场的一致性，同时施加全变和非负约束。我们提出了一种近端拟牛顿法来解决由此产生的子问题，并设计了一个自动参数选择程序来确定每个子问题的约束。我们验证了我们的方法在合成低分辨率幻影上的性能，并在高分辨率幻影上进行了不匹配的前向模型测试。