Alternating Phase Projected Gradient Descent with Generative Priors for Solving Compressive Phase Retrieval
This work addresses phase retrieval in signal acquisition systems, offering a novel method that improves upon existing approaches for this specific domain, though it appears incremental as it builds on prior techniques.
The authors tackled the ill-posed phase retrieval problem by replacing traditional sparsity priors with generative priors, proposing two algorithms that combine AltMin and projected gradient descent approaches, and empirically showing superior performance with an analysis of sample complexity for Gaussian measurements.
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.