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首页> 外文期刊>Inverse Problems: An International Journal of Inverse Problems, Inverse Methods and Computerised Inversion of Data >Inverse scattering in inhomogeneous background media: II. Multi-frequency case and SVD formulation
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Inverse scattering in inhomogeneous background media: II. Multi-frequency case and SVD formulation

机译:在不均匀背景介质中的逆散射:II。多频情况和SVD公式

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摘要

The inverse scattering problem formulated and solved within the distorted wave Born approximation (DWBA) in [1] (hereafter referred to as 'part I') is reformulated so as to be applicable to arbitrary (non-point) transmitter and receiver array elements and to frequency-independent (dispersionless) scattering potentials interrogated in a set of scattering experiments employing multiple temporal frequencies. The underlying structure of the pseudo-inverse reconstruction algorithm developed in part I is also revamped by use of the SVD so as to employ an orthonormal basis in the Hilbert space of compactly supported scattering potentials. This basis replaces the linearly dependent set of spanning functions used in part I and results in a more efficient reconstruction algorithm both in terms of CPU execution time as well as required computer storage space. Computer simulations illustrating the performance of the reformulated algorithm are presented.
机译:在[1]中的失真波博恩近似(DWBA)(以下称为“ I部分”)中公式化和求解的逆散射问题经过重新公式化,从而适用于任意(非点)发射器和接收器阵列元件,以及在一组使用多个时间频率的散射实验中被询问的与频率无关的(无色散)散射电位。第一部分中开发的伪逆重构算法的底层结构也通过使用SVD进行了修改,以便在紧致支持的散射势的希尔伯特空间中采用正交基础。此基础取代了第一部分中使用的线性相关的生成函数集,从而在CPU执行时间以及所需的计算机存储空间方面都产生了更有效的重构算法。给出了计算机模拟,该计算机模拟说明了重新制定的算法的性能。

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