On the Injectivity of STFT Phase Retrieval with super-exponential decaying window function

2025/11/19 by Shuang Guan, Kasso A. Okoudjou, Guan, Shuang +1
Mathematics · Physics and Astronomy · #Advanced X-ray Imaging Techniques #Digital Holography and Microscopy #Numerical methods in inverse problems #math.CA #math.CV #math.FA

paper · pdf · doi:10.48550/arxiv.2511.15894

openalex publication_date 2025/11/19 · openalex created_date 2025/11/23 · openalex updated_date 2026/07/28

Abstract

We investigate the uniqueness of short-time Fourier transform phase retrieval problems in L²(ℝ). In particular, for underlying window functions whose Fourier transform decay faster than any exponential function, we derive sufficient conditions on discrete sampling sets for unique phase retrieval from the spectrogram. This result generalizes previous uniqueness guarantees on sampling sets for Gaussian windows.

Citations

• Phase Retrieval via Wirtinger Flow: Theory and Algorithms

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