We characterize the measurement complexity of compressed sensing of signals
drawn from a known prior distribution, even when the support of the prior is
the entire space (rather than, say, sparse vectors). We show for Gaussian
measurements and \emph{any} prior distribution on the signal, that the
posterior sampling estimator achieves near-optimal recovery guarantees.
Moreover, this result is robust to model mismatch, as long as the distribution
estimate (e.g., from an invertible generative model) is close to the true
distribution in Wasserstein distance. We implement the posterior sampling
estimator for deep generative priors using Langevin dynamics, and empirically
find that it produces accurate estimates with more diversity than MAP.

本研究研究了来自已知先验分布的信号的压缩感知的测量复杂性，即使先验的支撑是整个空间（而不是稀疏向量）。对于高斯测量和信号上的任何先验分布，我们展示了后验抽样估计器可以实现近乎最优的恢复保证，在模型不匹配的情况下，只要分布估计（例如，从可逆生成模型中）与 Wasserstein 距离中的真实分布接近。我们使用 Langevin 动力学为深度生成先验实现了后验抽样估计器，并实验性地发现，它产生的准确估计具有比 MAP 更多的多样性。