2020/11/26 by Wei Qu, Xiaoyun Sun, Qu, Wei +3
Materials Science · Physics and Astronomy · #30H10 #42Axx #Advanced X-ray Imaging Techniques #Complex Variables (math.CV) #Electron and X-Ray Spectroscopy Techniques #FOS: Mathematics #X-ray Spectroscopy and Fluorescence Analysis
paper · pdf · doi:10.48550/arxiv.2011.13924
openalex publication_date 2020/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper concerns the study of reconstructing a function f in the Hardy space of the unit disc \D from intensity measurements |f(z)|, z∈ \D. It's known as the problem of phase retrieval. We transform it into solving the corresponding outer and inner function through the Nevanlinna factorization Theorem. The outer function will be established based on the mechanical quadrature method, while we use two different ways to find out the zero points of Blashcke product, thereby computing the inner function under the assumption that the singular inner function part is trivial. Then the concrete algorithms and illustrative experiments follow. Finally, we give a sparse representation of f by introducing the unwinding adaptive Fourier decomposition.