发表机构
University of Electronic Science and Technology of China（电子科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对带先验的噪声1比特压缩感知，证明后验采样的恢复上界与下界几乎匹配，通过带扩散先验的即插即用算法实现后验采样，在FFHQ、ImageNet数据集上验证了方法有效性。
AI 中文摘要
我们研究了基于先验分布的信号在噪声1比特压缩感知中的样本复杂度。通过近似覆盖数刻画先验的有效分布复杂度，我们证明当测量数随近似覆盖数的对数（乘以1比特分离间隙因子）缩放时，后验采样能以高概率实现精确恢复。该上界对学习到的先验不匹配具有鲁棒性：只要学习到的先验分布与真实信号分布在Wasserstein距离上足够接近，带近似先验的后验采样仍可靠。此外，我们建立了噪声1比特压缩感知任意可靠方法的样本复杂度下界，表明我们的上界在依赖先验的主要项上几乎匹配该下界。为近似现实场景中的理想后验采样过程，我们通过带扩散先验的即插即用算法实现后验采样。在FFHQ和ImageNet数据集上的实验验证了所提方法的有效性。
英文摘要
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.
CommentsAccepted to NeurIPS 2026 (poster)
