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Abstract：
We propose an artificial intelligence approach based on deep neural networks to tackle a canonical 2D scalar inverse source problem. The learned singular value decomposition (L-SVD) based on hybrid autoencoding is considered. We compare the reconstruction performance of L-SVD to the Truncated SVD (TSVD) regularized inversion, which is a canonical regularization scheme, to solve an ill-posed linear inverse problem. Numerical tests referring to far-field acquisitions show that L-SVD provides, with proper training on a well-organized dataset, superior performance in terms of reconstruction errors as compared to TSVD, allowing for the retrieval of faster spatial variations of the source. Indeed, L-SVD accommodates a priori information on the set of relevant unknown current distributions. Different from TSVD, which performs linear processing on a linear problem, L-SVD operates non-linearly on the data. A numerical analysis also underlines how the performance of the L-SVD degrades when the unknown source does not match the training dataset.
摘要：
我们提出了一种基于深度神经网络的人工智能方法来解决规范的2D标量反源问题。考虑了基于混合自动编码的学习奇异值分解（L-SVD）。我们比较了L-SVD与截断SVD（TSVD）正则化反演的重建性能，这是一个规范的正则化方案，求解一个不适定线性逆问题。参考远场采集的数值测试表明，L-SVD提供了，在组织良好的数据集上进行适当的培训，与TSVD相比，在重建误差方面表现优异，允许检索源的更快空间变化。的确,L-SVD容纳关于相关未知电流分布的集合的先验信息。与TSVD不同，对线性问题进行线性处理，L-SVD对数据进行非线性操作。数值分析还强调了当未知源与训练数据集不匹配时L-SVD的性能如何下降。
