Instance-Optimal Compressed Sensing via Posterior Sampling
Instance-Optimal Compressed Sensing via Posterior Sampling
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发表时间：
2021-06
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通讯作者：
A. Jalal;Sushrut Karmalkar;A. Dimakis;Eric Price
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作者：
A. Jalal;Sushrut Karmalkar;A. Dimakis;Eric Price
我们描述了从已知先验分布中提取的信号的压缩感知的测量复杂性，即使先验的支持是整个空间（而不是稀疏向量）。我们证明，对于信号的高斯测量和 \emph{any} 先验分布，后验采样估计器实现了接近最优的恢复保证。此外，只要分布估计（例如，来自可逆生成模型）接近 Wasserstein 距离的真实分布，该结果对于模型失配是稳健的。我们使用 Langevin 动力学实现深度生成先验的后验采样估计器，并根据经验发现它可以产生比 MAP 更具多样性的准确估计。
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.