Focusing and imaging using eigenfunctions of the scattering operator
Focusing and imaging using eigenfunctions of the scattering operator
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DOI：
10.1121/1.419898
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发表时间：
1997-08-01
影响因子：
2.4
通讯作者：
Waag, RC
中科院分区：
文献类型：
--
作者：
Mast, TD;Nachman, AI;Waag, RC
提出了一种利用散射算子本征函数的逆散射方法。这种方法提供了一个统一的框架，包括本征函数方法的聚焦和定量图像重建在任意介质。散射声场描述使用一个紧凑的，正常的运营商，该运营商的本征函数示出对应于源分布的远场模式，直接成比例的散射对象的位置相关的对比度。相反，散射算子的本征函数指定入射波模式，集中在这些有效的源分布。这些聚焦特性被用于一种新的逆散射方法，该方法使用数值计算的本征函数场的乘积来表示未知的散射介质。一个正规化的解决方案的非线性逆散射问题的结果，从这些产品的组合，使产品包括一个自然的基础，高效和准确的重建未知的不均匀性。相应的线性化问题解析求解，得到一个简单的低通滤波散射势公式。该线性公式与已知的滤波反向传播玻恩反演公式在解析上等价，至少在小散射体的情况下，具有计算简单和效率高的优点。一个类似的有效和简单的公式推导出的非线性问题，其中的总声压可以确定的基础上估计的介质。计算结果表明，本征函数的离散和分布式散射介质，定量成像的非均匀介质使用产品的重传本征函数，在非均匀背景介质中的逆散射，和重建数据被噪声破坏的重点。(C)1997年美国声学学会。
An inverse scattering method that uses eigenfunctions of the scattering operator is presented. This approach provides a unified framework that encompasses eigenfunction methods of focusing and quantitative image reconstruction in arbitrary media. Scattered acoustic fields are described using a compact, normal operator, The eigenfunctions of this operator are shown to correspond to the far-field patterns of source distributions that are directly proportional to the position-dependent contrast of a scattering object. Conversely, the eigenfunctions of the scattering operator specify incident-wave patterns that focus on these effective source distributions. These focusing properties are employed in a new inverse scattering method that represents unknown scattering media using products of numerically calculated fields of eigenfunctions. A regularized solution to the nonlinear inverse scattering problem is shown to result from combinations of these products, so that the products comprise a natural basis for efficient and accurate reconstructions of unknown inhomogeneities. The corresponding linearized problem is solved analytically, resulting in a simple formula for the low-pass-filtered scattering potential, The linear formula is analytically equivalent to known filtered-backpropagation formulas for Born inversion, and, at least in the case of small scattering objects, has advantages of computational simplicity and efficiency. A similarly efficient and simple formula is derived for the nonlinear problem in which the total acoustic pressure can be determined based on an estimate of the medium. Computational results illustrate focusing of eigenfunctions on discrete and distributed scattering media, quantitative imaging of inhomogeneous media using products of retransmitted eigenfunctions, inverse scattering in an inhomogeneous background medium, and reconstructions for data corrupted by noise. (C) 1997 Acoustical Society of America.