论文标题
以未知方向压缩感测的模棱两可的先验
Equivariant Priors for Compressed Sensing with Unknown Orientation
论文作者
论文摘要
在压缩感应中，目标是从不确定的线性测量系统中重建信号。因此，需要有关感兴趣信号及其结构的先验知识。此外，在许多情况下，该信号在测量之前具有未知的方向。为了解决此类恢复问题，我们建议使用Equivariant生成模型作为先验，该模型将定向信息封装在其潜在空间中。因此，我们表明，具有未知取向的信号可以通过这些模型潜在空间的迭代梯度下降来恢复，并提供额外的理论恢复保证。我们构建了一个模棱两可的变性自动编码器，并将解码器用作压缩传感的生成性先验。我们讨论了融合和潜伏期的拟议方法的其他潜在收益。
In compressed sensing, the goal is to reconstruct the signal from an underdetermined system of linear measurements. Thus, prior knowledge about the signal of interest and its structure is required. Additionally, in many scenarios, the signal has an unknown orientation prior to measurements. To address such recovery problems, we propose using equivariant generative models as a prior, which encapsulate orientation information in their latent space. Thereby, we show that signals with unknown orientations can be recovered with iterative gradient descent on the latent space of these models and provide additional theoretical recovery guarantees. We construct an equivariant variational autoencoder and use the decoder as generative prior for compressed sensing. We discuss additional potential gains of the proposed approach in terms of convergence and latency.
