2016/10/22 by Pfander, Goetz E., Palina Salanevich, Salanevich, Palina
Computer Science · Engineering · Physics and Astronomy · #Advanced Measurement and Metrology Techniques #Advanced X-ray Imaging Techniques #FOS: Mathematics #Functional Analysis (math.FA) #Optical measurement and interference techniques
paper · pdf · doi:10.48550/arxiv.1611.02540
openalex publication_date 2016/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We address the problem of signal reconstruction from intensity measurements\nwith respect to a measurement frame. This non-convex inverse problem is known\nas phase retrieval. The case considered in this paper concerns phaseless\nmeasurements taken with respect to a Gabor frame. It arises naturally in many\npractical applications, such as diffraction imaging and speech recognition. We\npresent a reconstruction algorithm that uses a nearly optimal number of\nphaseless time-frequency structured measurements and discuss its robustness in\nthe case when the measurements are corrupted by noise. We show how geometric\nproperties of the measurement frame are related to the robustness of the\nphaseless reconstruction. The presented algorithm is based on the idea of\npolarization as proposed by Alexeev, Bandeira, Fickus, and Mixon.\n