This paper considers the problem of recovering signals modeled by generative models from linear measurements contaminated with sparse outliers. We propose an outlier detection approach for reconstructing the ground-truth signals modeled by generative models under sparse outliers. We establish theoretical recovery guarantees for reconstruction of signals using generative models in the presence of outliers, giving lower bounds on the number of correctable outliers. Our results are applicable to both linear generator neural networks and the nonlinear generator neural networks with an arbitrary number of layers. We propose an iterative alternating direction method of multipliers (ADMM) algorithm for solving the outlier detection problem via $\ell_1$ norm minimization, and a gradient descent algorithm for solving the outlier detection problem via squared $\ell_1$ norm minimization. We conduct extensive experiments using variational auto-encoder and deep convolutional generative adversarial networks, and the experimental results show that the signals can be successfully reconstructed under outliers using our approach. Our approach outperforms the traditional Lasso and $\ell_2$ minimization approach.

翻译：本文研究了从含有稀疏异常值的线性测量中恢复由生成模型建模信号的问题。我们提出了一种异常值检测方法，用于在稀疏异常值存在下重建由生成模型建模的真实信号。我们建立了在异常值存在下使用生成模型重建信号的理论恢复保证，给出了可纠正异常值数量的下界。我们的结果适用于具有任意层数的线性生成器神经网络和非线性生成器神经网络。我们提出了一种通过$\ell_1$范数最小化解决异常值检测问题的迭代交替方向乘子法（ADMM）算法，以及一种通过平方$\ell_1$范数最小化解决异常值检测问题的梯度下降算法。我们使用变分自编码器和深度卷积生成对抗网络进行了大量实验，实验结果表明，我们的方法能够在存在异常值的情况下成功重建信号。与传统Lasso和$\ell_2$最小化方法相比，我们的方法具有更优的性能。