Stable phase retrieval for Hermite-Fock expansions

Source: url:https://github.com/susannabertolini/PhaseRetrieval Authors: Susanna Bertolini, Jaume de Dios Pont Status: verified Main declarations: DimdPolyShowcaseChallenge.stable_phase_retrieval Tags: phase-retrieval, hermite-fock, gaussian-measure, complex-analysis MSC: 42C05, 46E22, 94A12

References

Stable phase retrieval is the problem of reconstructing a signal from the magnitudes of its frame/expansion coefficients up to a single global phase, with a uniform stability constant under noise. For the named problem and its stability theory see R. Balan, P. Casazza, and D. Edidin, On signal reconstruction without phase, Appl. Comput. Harmon. Anal. 20 (2006), 345-356 (doi:10.1016/j.acha.2005.07.001), and J. Cahill, P. Casazza, and I. Daubechies, Phase retrieval in infinite-dimensional Hilbert spaces, Trans. Amer. Math. Soc. Ser. B 3 (2016), 63-76. This project formalises a fixed-dimensional stable phase-retrieval theorem for the Gaussian L^2 closure of Hermite-Fock polynomials.