On Recovery Guarantees for One-Bit Compressed Sensing on Manifolds

@article{Iwen2018OnRG,
title={On Recovery Guarantees for One-Bit Compressed Sensing on Manifolds},
author={Mark A. Iwen and Felix Krahmer and Sara Krause-Solberg and Johannes Maly},
journal={Discrete \& Computational Geometry},
year={2018},
volume={65},
pages={953 - 998}
}
• Published 17 July 2018
• Computer Science, Mathematics
• Discrete & Computational Geometry
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…
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An upper bound on the recovery error is proved which outperforms prior works that use memoryless scalar quantization, requires a simpler analysis, and extends the class of measurements beyond Gaussians.
• Computer Science, Mathematics
2019 13th International conference on Sampling Theory and Applications (SampTA)
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Two computationally efficient reconstruction algorithms that only require access to a geometric multi-resolution analysis approximation of the manifold are introduced that are robust with respect to both pre- and post-quantization noise.
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This work proposes to estimate the signals via a convex program based on rectified linear units (ReLUs) for two different quantization schemes, namely one-bit and uniform multi-bit quantization, and shows that the program is robust against adversarial bit corruptions as well as additive noise on the linear measurements.