中文

$L^2$-Stability for STFT phase retrieval

泛函分析 2026-05-21 v1 经典分析与常微分方程

摘要

We prove that the short-time Fourier transform with Gaussian window performs L2L^2-local stable phase retrieval at the constant function. The proof involved significant interplay between mathematicians and LLMs. An autoformalization in Lean 4 of an extension of our result to L2L^2-local stable phase retrieval for all Hermite windows and all elements in the finite span of the canonical basis vectors is also presented.

引用

@article{arxiv.2605.20527,
  title  = {$L^2$-Stability for STFT phase retrieval},
  author = {Susanna Bertolini and Jaume de Dios Pont and Ben Pineau and Mitchell A. Taylor and João P. G. Ramos},
  journal= {arXiv preprint arXiv:2605.20527},
  year   = {2026}
}

备注

24 pages, accpmpaining Lean source code in https://github.com/susannabertolini/PhaseRetrieval