2024/12/10 by Peng, Haiyang, Han, Deren, Linbin Li +3 · 1 citation
Computer Science · Earth and Planetary Sciences · Physics and Astronomy · #90C26 #90C30 #94A12 #Advanced X-ray Imaging Techniques #FOS: Mathematics #Optical measurement and interference techniques #Optimization and Control (math.OC) #Seismic Imaging and Inversion Techniques
paper · pdf · doi:10.48550/arxiv.2412.07401
openalex publication_date 2024/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper aims to address the phase retrieval problem from subgaussian measurements with arbitrary noise, with a focus on devising robust and efficient algorithms for solving non-convex problems. To ensure uniqueness of solutions in the subgaussian setting, we explore two commonly used assumptions: either the subgaussian measurements satisfy a fourth-moment condition or the target signals exhibit non-peakiness. For each scenario, we introduce a novel spectral initialization method that yields robust initial estimates. Building on this, we employ leave-one-out arguments to show that the classical Wirtinger flow algorithm achieves a linear rate of convergence for both real-valued and complex-valued cases, provided the sampling complexity m≥ O(n log3 m), where n is the dimension of the underlying signals. In contrast to existing work, our algorithms are regularization-free, requiring no truncation, trimming, or additional penalty terms, and they permit the algorithm step sizes as large as O(1), compared to the O(1/n) in previous literature. Furthermore, our results accommodate arbitrary noise vectors that meet certain statistical conditions, covering a wide range of noise scenarios, with sub-exponential noise as a notable special case. The effectiveness of our algorithms is validated through various numerical experiments. We emphasize that our findings provide the first theoretical guarantees for recovering non-peaky signals using non-convex methods from Bernoulli measurements, which is of independent interest.