A Sparsity Regularization Approach to the Electromagnetic Inverse Scattering Problem.
A Sparsity Regularization Approach to the Electromagnetic Inverse Scattering Problem.
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DOI：
10.1109/tap.2009.2035997
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发表时间：
2010-01-01
影响因子：
5.7
通讯作者：
Hagness SC
中科院分区：
文献类型：
--
作者：
Winters DW;Van Veen BD;Hagness SC
我们研究使用扭曲玻恩迭代法 (DBIM) 结合称为弹性网络的变量选择方法来解决电磁逆散射问题。弹性网络应用 和 罚分来规范 DBIM 每次迭代时产生的线性方程组。因此，弹性网结合了惩罚的稳定作用和惩罚的稀疏鼓励作用。当介电特性的未知分布在一组已知的基函数中稀疏时，具有弹性网络的 DBIM 的性能优于常用的正则化器。我们考虑两个截然不同的 3D 示例来证明我们方法的有效性和适用性。对于这两个示例，我们在逆解中使用标量近似。在第一个示例中，介电特性的实际分布在一组 3-D 小波中完全是稀疏的。将弹性网络和方法的性能与先验已知真实解中涉及哪些小波的理想情况进行比较。第二个例子来自用于乳腺癌检测的微波成像领域。对于给定的一组 3-D 高斯基函数，我们表明弹性网络方法可以对解剖学上真实的 3-D 数值乳房模型内的介电特性（特别是有效电导率）的分布进行更准确的估计。相比之下，带有惩罚的 DBIM 产生的估计会受到多个工件的影响。
We investigate solving the electromagnetic inverse scattering problem using the distorted Born iterative method (DBIM) in conjunction with a variable-selection approach known as the elastic net. The elastic net applies both and penalties to regularize the system of linear equations that result at each iteration of the DBIM. The elastic net thus incorporates both the stabilizing effect of the penalty with the sparsity encouraging effect of the penalty. The DBIM with the elastic net outperforms the commonly used regularizer when the unknown distribution of dielectric properties is sparse in a known set of basis functions. We consider two very different 3-D examples to demonstrate the efficacy and applicability of our approach. For both examples, we use a scalar approximation in the inverse solution. In the first example the actual distribution of dielectric properties is exactly sparse in a set of 3-D wavelets. The performances of the elastic net and approaches are compared to the ideal case where it is known a priori which wavelets are involved in the true solution. The second example comes from the area of microwave imaging for breast cancer detection. For a given set of 3-D Gaussian basis functions, we show that the elastic net approach can produce a more accurate estimate of the distribution of dielectric properties (in particular, the effective conductivity) within an anatomically realistic 3-D numerical breast phantom. In contrast, the DBIM with an penalty produces an estimate which suffers from multiple artifacts.
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影响因子：
5.7
作者：
De Zaeytijd, Juergen;Franchois, Ann;Geffrin, Jean-Michel
通讯作者：
Geffrin, Jean-Michel
影响因子：
3
作者：
Donoho, DL
通讯作者：
Donoho, DL
影响因子：
8.2
作者：
Cui, TJ;Chew, WC;Chen, SY
通讯作者：
Chen, SY
影响因子：
2.5
作者：
HOERL, AE;KENNARD, RW
通讯作者：
KENNARD, RW
影响因子：
3.1
作者：
HANSEN, PC;OLEARY, DP
通讯作者：
OLEARY, DP