论文标题
使用生成模型的强大压缩感测
Robust Compressed Sensing using Generative Models
论文作者
论文摘要
压缩感测的目的是从噪音线性方程不确定的系统中估算高维矢量。与经典压缩传感相比，在这里，我们假设一个生成模型为先验，也就是说，我们假设向量由深的生成模型$ g：\ mathbb {r}^k \ rightarrow \ rightarrow \ mathbb {r}^n $表示。当测量矩阵是高豪斯级时，可以保证诸如经验风险最小化（ERM）之类的经典恢复方法。但是，当测量矩阵和测量值是重尾或有离群值时，恢复可能会发生巨大失败。在本文中，我们提出了一种受均值（妈妈）启发的算法。即使在存在异常值的情况下，我们的算法也保证了重尾数据的恢复。从理论上讲，我们的结果表明，基于妈妈的新算法具有与高斯以下假设相同的样本复杂性保证。我们的实验验证了我们主张的两个方面：其他算法确实是脆弱的，并且在重尾和/或损坏的数据下失败，而我们的方法表现出预测的鲁棒性。
The goal of compressed sensing is to estimate a high dimensional vector from an underdetermined system of noisy linear equations. In analogy to classical compressed sensing, here we assume a generative model as a prior, that is, we assume the vector is represented by a deep generative model $G: \mathbb{R}^k \rightarrow \mathbb{R}^n$. Classical recovery approaches such as empirical risk minimization (ERM) are guaranteed to succeed when the measurement matrix is sub-Gaussian. However, when the measurement matrix and measurements are heavy-tailed or have outliers, recovery may fail dramatically. In this paper we propose an algorithm inspired by the Median-of-Means (MOM). Our algorithm guarantees recovery for heavy-tailed data, even in the presence of outliers. Theoretically, our results show our novel MOM-based algorithm enjoys the same sample complexity guarantees as ERM under sub-Gaussian assumptions. Our experiments validate both aspects of our claims: other algorithms are indeed fragile and fail under heavy-tailed and/or corrupted data, while our approach exhibits the predicted robustness.
