论文标题
用于解决非线性反问题的数据一致的神经网络
Data-consistent neural networks for solving nonlinear inverse problems
论文作者
论文摘要
包含训练有素的神经网络的数据辅助重建算法是解决反问题的新型范式。一种方法是首先采用经典的重建方法，然后应用神经网络来改善其解决方案。经验证据表明，这种两步方法提供了高质量的重建，但它们缺乏融合分析。在本文中，我们将这种两步方法正式使用经典正则化理论。我们提出了与经典正则化方法相结合的数据一致的神经网络。这产生了一种数据驱动的正则化方法，我们为噪声提供了完整的收敛分析。数值模拟表明，与标准的两步深度学习方法相比，我们的方法在测试集中的结构变化方面提供了更好的稳定性，同时在测试数据上类似地执行与训练集相似的执行。我们的方法提供了一个稳定的逆问题解决方案，可以利用已知的非线性正向模型以及数据中所需的解决方案歧管。
Data assisted reconstruction algorithms, incorporating trained neural networks, are a novel paradigm for solving inverse problems. One approach is to first apply a classical reconstruction method and then apply a neural network to improve its solution. Empirical evidence shows that such two-step methods provide high-quality reconstructions, but they lack a convergence analysis. In this paper we formalize the use of such two-step approaches with classical regularization theory. We propose data-consistent neural networks that we combine with classical regularization methods. This yields a data-driven regularization method for which we provide a full convergence analysis with respect to noise. Numerical simulations show that compared to standard two-step deep learning methods, our approach provides better stability with respect to structural changes in the test set, while performing similarly on test data similar to the training set. Our method provides a stable solution of inverse problems that exploits both the known nonlinear forward model as well as the desired solution manifold from data.
