Robust one-bit compressed sensing with non-Gaussian measurements
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We study memoryless one-bit compressed sensing with non-Gaussian measurement matrices. We show that by quantizing at uniformly distributed thresholds, it is possible to accurately reconstruct low-complexity signals from a small number of one-bit quantized measurements, even if the measurement vectors are drawn from a heavy-tailed distribution. Our reconstruction results are uniform in nature and robust in the presence of pre-quantization noise on the analog measurements as well as adversarial bit corruptions in the quantization process. If the measurement matrix is subgaussian, then accurate recovery can be achieved via a convex program. Our reconstruction theorems rely on a new random hyperplane tessellation result, which is of independent interest.
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