论文标题
通过模棱两可的神经网络解决宽带反向散射问题
Solving the Wide-band Inverse Scattering Problem via Equivariant Neural Networks
论文作者
论文摘要
本文介绍了一种新型的深神经网络结构，用于通过直接近似逆映射来解决频域中的反向散射问题，从而避免了经典方法的昂贵优化环路。该体系结构是由完整的孔径和均匀背景中过滤后的反射公式进行的，它利用了问题的基本等效性和积分操作员的可压缩性。这大大减少了训练参数的数量，因此该方法的计算和样品复杂性。特别是，我们获得了一个体系结构，其参数数量相对于输入的维度，其推理复杂性超级线性缩放超级线性，但具有很小的常数。我们提供了几种数值测试，这些测试表明，当前方法比基于优化的技术（例如全波倒置）会导致更好的重建，但是在与最先进的机器学习方法竞争的同时，成本的一小部分。
This paper introduces a novel deep neural network architecture for solving the inverse scattering problem in frequency domain with wide-band data, by directly approximating the inverse map, thus avoiding the expensive optimization loop of classical methods. The architecture is motivated by the filtered back-projection formula in the full aperture regime and with homogeneous background, and it leverages the underlying equivariance of the problem and compressibility of the integral operator. This drastically reduces the number of training parameters, and therefore the computational and sample complexity of the method. In particular, we obtain an architecture whose number of parameters scale sub-linearly with respect to the dimension of the inputs, while its inference complexity scales super-linearly but with very small constants. We provide several numerical tests that show that the current approach results in better reconstruction than optimization-based techniques such as full-waveform inversion, but at a fraction of the cost while being competitive with state-of-the-art machine learning methods.
