This paper studies the problem of recovering a signal from one-bit compressed sensing measurements under a manifold model; that is, assuming that the signal lies on or near a manifold of low intrinsic dimension. We provide a convex recovery method based on the Geometric Multi-Resolution Analysis and prove recovery guarantees with a near-optimal scaling in the intrinsic manifold dimension. Our method is the first tractable algorithm with such guarantees for this setting. The results are complemented by numerical experiments confirming the validity of our approach.

中文翻译：

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关于流形上一位压缩感知的恢复保证

本文研究了在流形模型下从一位压缩传感测量中恢复信号的问题。也就是说，假设信号位于低固有尺寸的歧管上或附近。我们提供了基于几何多分辨率分析的凸恢复方法，并证明了在固有流形维数上具有接近最佳缩放比例的恢复保证。我们的方法是第一个具有这种设置保证的易处理算法。数值实验对结果进行了补充，证实了我们方法的有效性。