Locating Multiple Multiscale Acoustic Scatterers
Locating Multiple Multiscale Acoustic Scatterers
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DOI：
10.1137/13093409x
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发表时间：
2014-07
期刊：
影响因子：
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通讯作者：
Jingzhi Li;Hongyu Liu;J. Zou
中科院分区：
文献类型：
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作者：
Jingzhi Li;Hongyu Liu;J. Zou
我们开发了三个逆散射计划定位多个多尺度声散射体在一个非常普遍和实用的设置。对于所有的三个定位方案，只有一个单一的远场测量使用。多个散射体成分的数量可以是未知的，并且每个散射体成分被允许是具有未知内容的非均匀介质或声软、声硬或阻抗类型的不可穿透的障碍物。此外，散射体可以是多尺度的;即，就检测声波的波长而言，一些散射体可以具有规则的尺寸，而另一些散射体可以具有较小的尺寸。如果散射体组件是规则的大小，它是必要的，它的形状（不一定是它的方向，大小和位置）应该是从一个可接受的类，这是事先已知的。定位方案是基于一些新的指示函数，计算成本低，对测量噪声的鲁棒性。严格的数学证明提供了.
We develop three inverse scattering schemes for locating multiple multiscale acoustic scatterers in a very general and practical setting. For all of the three locating schemes, only one single far-field measurement is used. The number of the multiple scatterer components may be unknown, and each scatterer component is allowed to be an inhomogeneous medium with an unknown content or an impenetrable obstacle of sound-soft, sound-hard, or impedance type. Moreover, the scatterers could be multiscale; i.e., some scatterers may be of regular size, and some others may be of small size in terms of the wavelength of the detecting acoustic wave. If a scatterer component is of regular size, it is required that its shape (not necessarily its orientation, size, and location) should be from an admissible class which is known in advance. The locating schemes are based on some novel indicator functions and are computationally cheap and robust against the measurement noise. Rigorous mathematical justifications are provide...