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arXiv · 1807.06490

On Recovery Guarantees for One-Bit Compressed Sensing on Manifolds

Mark A. Iwen·Felix Krahmer·Sara Krause-Solberg·Johannes Maly
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Abstract

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.

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Mark A. Iwen, Felix Krahmer, Sara Krause-Solberg, Johannes Maly. 2018-07-17. On Recovery Guarantees for One-Bit Compressed Sensing on Manifolds. https://arxiv.org/abs/1807.06490

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