الملخص
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 distance. In addition, we establish a sample complexity lower bound for any reliable method of noisy one-bit compressed sensing, showing that our upper bound is nearly matched in its main prior dependent term. To approximate the ideal posterior sampling process for real world scenarios, we instantiate posterior sampling through a plug-and-play algorithm with diffusion priors. Experiments on the FFHQ and ImageNet datasets demonstrate the effectiveness of our proposed approach.
الكلمات المفتاحية
الموضوع
بيانات النشر
- المجلة
- غير متاح
- وصول مفتوح
- وصول مفتوح أخضر
اقتبس هذه المقالة
APA 7
Ma, J., Wu, Y., & Liu, Z. (2026). Recovery Guarantees for Posterior Sampling of One-Bit Compressed Sensing. https://omanscience.com/ar/articles/recovery-guarantees-for-posterior-sampling-of-one-bit-compressed-sensing
MLA 9
Ma, Jing, et al. "Recovery Guarantees for Posterior Sampling of One-Bit Compressed Sensing." https://omanscience.com/ar/articles/recovery-guarantees-for-posterior-sampling-of-one-bit-compressed-sensing.
شيكاغو (المؤلف–التاريخ)
Ma, Jing, Yujia Wu, and Zhaoqiang Liu. 2026. "Recovery Guarantees for Posterior Sampling of One-Bit Compressed Sensing." https://omanscience.com/ar/articles/recovery-guarantees-for-posterior-sampling-of-one-bit-compressed-sensing.
هارفارد
Ma, J., Wu, Y. and Liu, Z. (2026) 'Recovery Guarantees for Posterior Sampling of One-Bit Compressed Sensing', Available at: https://omanscience.com/ar/articles/recovery-guarantees-for-posterior-sampling-of-one-bit-compressed-sensing.
فانكوفر
Ma J, Wu Y, Liu Z. Recovery Guarantees for Posterior Sampling of One-Bit Compressed Sensing. https://omanscience.com/ar/articles/recovery-guarantees-for-posterior-sampling-of-one-bit-compressed-sensing
IEEE
J. Ma, Y. Wu, and Z. Liu, "Recovery Guarantees for Posterior Sampling of One-Bit Compressed Sensing," https://omanscience.com/ar/articles/recovery-guarantees-for-posterior-sampling-of-one-bit-compressed-sensing.