Abstract
The classical problem of phase retrieval arises in various signal acquisition systems. Due to the ill-posed nature of the problem, the solution requires assumptions on the structure of the signal. In the last several years, sparsity and support-based priors have been leveraged successfully to solve this problem. In this work, we propose replacing the sparsity/support priors with generative priors and propose two algorithms to solve the phase retrieval problem. Our proposed algorithms combine the ideas from AltMin approach for non-convex sparse phase retrieval and projected gradient descent approach for solving linear inverse problems using generative priors. We empirically show that the performance of our method with projected gradient descent is superior to the existing approach for solving phase retrieval under generative priors. We support our method with an analysis of sample complexity with Gaussian measurements.
Abstract (translated)
在各种信号采集系统中出现了经典的相位恢复问题。由于问题的不适定性质，解决方案需要对信号结构进行假设。近年来，利用稀疏性和基于支持的先验理论成功地解决了这一问题。在这项工作中，我们提出用生成先验代替稀疏/支持先验，并提出两种算法来解决相位检索问题。我们提出的算法结合了非凸稀疏相位检索的Altmin方法和投影梯度下降法的思想，利用生成先验来求解线性逆问题。实验表明，投影梯度下降法的性能优于现有的生成先验条件下的相位恢复方法。我们支持使用高斯测量分析样本复杂性的方法。
URL
https://arxiv.org/abs/1903.02707
