论文标题
使用生成模型从非线性观察中恢复非著名的恢复
Non-Iterative Recovery from Nonlinear Observations using Generative Models
论文作者
论文摘要
在本文中，我们旨在估算出在半参数单索引模型（SIM）之后从其非线性观测值的基础信号的方向。与传统的压缩传感相比，假定信号是稀疏的，我们假设该信号位于$ l $ -lipschitz连续生成模型的范围内，具有有限的$ k $二维输入。这主要是由于深层生成模型在各种真实应用中取得了巨大成功的推动。我们的重建方法是非涉及的（尽管近似投影步骤可能会使用迭代过程）并且高效，并且显示出可以达到近乎最佳的统计率$ \ sqrt {（k \ log l）/m} $，如果$ m $是$ m $的测量数。我们考虑了SIM的两个特定实例，即嘈杂的$ 1 $ - 位和立方测量模型，并在图像数据集上执行实验以证明我们方法的功效。特别是，对于嘈杂的$ 1 $数量测量模型，我们表明，就准确性和效率而言，我们的非著作方法显着优于最先进的迭代方法。
In this paper, we aim to estimate the direction of an underlying signal from its nonlinear observations following the semi-parametric single index model (SIM). Unlike conventional compressed sensing where the signal is assumed to be sparse, we assume that the signal lies in the range of an $L$-Lipschitz continuous generative model with bounded $k$-dimensional inputs. This is mainly motivated by the tremendous success of deep generative models in various real applications. Our reconstruction method is non-iterative (though approximating the projection step may use an iterative procedure) and highly efficient, and it is shown to attain the near-optimal statistical rate of order $\sqrt{(k \log L)/m}$, where $m$ is the number of measurements. We consider two specific instances of the SIM, namely noisy $1$-bit and cubic measurement models, and perform experiments on image datasets to demonstrate the efficacy of our method. In particular, for the noisy $1$-bit measurement model, we show that our non-iterative method significantly outperforms a state-of-the-art iterative method in terms of both accuracy and efficiency.
