Recovery Guarantees for Posterior Sampling of One-Bit Compressed Sensing
We study the sample complexity of noisy one-bit compressed sensing for signals drawn from a prior distribution. By characterizing the effective distributional complexity of the prior via its approximate covering number, we prove that posterior sampling achieves accurate recovery with high probability when the number of measurements scales with the logarithm of the approximate covering number, up to a one-bit separation gap factor. This upper bound is robust to learned prior mismatch. Specifically, we show that posterior sampling with an approximate prior remains reliable, provided that the learned prior distribution is sufficiently close to the true signal distribution in Wasserstein dist...
| Authors | Jing Ma, Yujia Wu, Zhaoqiang Liu |
|---|---|
| Primary category | cs.LG |
| Published | 8 October 2026 |
| Last updated at source | 12 October 2026 |
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