6 citations · 9 across the 8 of their papers we have counts for
7 papers · 1 filter
Sobolev-type embeddings for neural network approximation spaces
Philipp Grohs, Felix Voigtlaender
We consider neural network approximation spaces that classify functions according to the rate at which they can be approximated (with error measured in ) by ReLU neural networ…
-stability analysis for Gabor phase retrieval
Philipp Grohs, Martin Rathmair
We consider the problem of reconstructing the missing phase information from spectrogram data with $$ \mathcal{G}f(x,y)=\int_\mathbb{R} f(t) e^{-π(t-x)^2}e^{-2πi…
Phase Transitions in Rate Distortion Theory and Deep Learning
Philipp Grohs, Andreas Klotz, Felix Voigtlaender
Rate distortion theory is concerned with optimally encoding a given signal class using a budget of bits, as . We say that can be compres…
Stable Gabor phase retrieval for multivariate functions
Philipp Grohs, Martin Rathmair
In recent work [P. Grohs and M. Rathmair. Stable Gabor Phase Retrieval and Spectral Clustering. Communications on Pure and Applied Mathematics (2018)] the instabilities of the Gabo…
Phase Retrieval: Uniqueness and Stability
Philipp Grohs, Sarah Koppensteiner, Martin Rathmair
The problem of phase retrieval, i.e., the problem of recovering a function from the magnitudes of its Fourier transform, naturally arises in various fields of physics, such as astr…
Gabor phase retrieval is severely ill-posed
Rima Alaifari, Philipp Grohs
The problem of reconstructing a function from the magnitudes of its frame coefficients has recently been shown to be never uniformly stable in infinite-dimensional spaces [5]. This…