Abstract

In light of recent work on continuous Gabor phase retrieval, we analyse discrete Gabor phase retrieval problems and note that under realistic decay assumptions on the window functions, the stability constants increase significantly in the space dimension. When using discretisations of the Gaussian as windows, we are in fact able to show that the stability constants grow at least exponentially as the dimension of the space increases. At the same time, we observe that the adversarial examples, which we construct to estimate the stability constants, all contain long modes of silence. This suggests that one should try to reconstruct signals up to so-called semi-global phase factors and not up to a global phase factor as is the canon in the literature. This observation is further corroborated by a stability result for discrete Gabor phase retrieval which we have proven recently.