标题： 具有部分高斯循环矩阵和生成先验的鲁棒1比特压缩传感 显示英文标题

标题： Robust 1-bit Compressive Sensing with Partial Gaussian Circulant Matrices and Generative Priors

摘要： 在一比特压缩感知中，每个测量值被量化为单个比特，即未知向量的线性函数的符号，目标是准确地恢复该向量。虽然在一比特压缩感知中最流行的是假设标准高斯传感矩阵，但由于结构化传感矩阵（如部分高斯循环矩阵）具有更快的矩阵运算速度，因此它们在实际应用中具有重要意义。本文针对随机符号的部分高斯循环矩阵和生成模型，为基于相关性的鲁棒一比特压缩感知优化算法提供了恢复保证。在适当的假设下，我们得到了之前仅适用于需要显著更多计算的独立同分布高斯矩阵的保证。我们利用一个实用的迭代算法，并在图像数据集上进行数值实验以验证我们的理论结果。 显示英文摘要

摘要： In 1-bit compressive sensing, each measurement is quantized to a single bit, namely the sign of a linear function of an unknown vector, and the goal is to accurately recover the vector. While it is most popular to assume a standard Gaussian sensing matrix for 1-bit compressive sensing, using structured sensing matrices such as partial Gaussian circulant matrices is of significant practical importance due to their faster matrix operations. In this paper, we provide recovery guarantees for a correlation-based optimization algorithm for robust 1-bit compressive sensing with randomly signed partial Gaussian circulant matrices and generative models. Under suitable assumptions, we match guarantees that were previously only known to hold for i.i.d.~Gaussian matrices that require significantly more computation. We make use of a practical iterative algorithm, and perform numerical experiments on image datasets to corroborate our theoretical results.