153 citations · 899 across the 45 of their papers we have counts for
6 papers · 1 filter
Stable Phase Retrieval in Infinite Dimensions
Rima Alaifari, Ingrid Daubechies, Philipp Grohs +1
The problem of phase retrieval is to determine a signal , with a Hilbert space, from intensity measurements , where $F(ω):=\langle f , φ_ω\r…
Discrete Deep Feature Extraction: A Theory and New Architectures
Thomas Wiatowski, Michael Tschannen, Aleksandar Stanić +2
First steps towards a mathematical theory of deep convolutional neural networks for feature extraction were made---for the continuous-time case---in Mallat, 2012, and Wiatowski and…
Convergence of a Strang splitting finite element discretization for the Schrödinger-Poisson equation
Winfried Auzinger, Thomas Kassebacher, Othmar Koch +1
Operator splitting methods combined with finite element spatial discretizations are studied for time-dependent nonlinear Schrödinger equations. In particular, the Schrödinger-Poiss…
Phase retrieval in the general setting of continuous frames for Banach spaces
Rima Alaifari, Philipp Grohs
We develop a novel and unifying setting for phase retrieval problems that works in Banach spaces and for continuous frames and consider the questions of uniqueness and stability of…
On the Approximation of Functions with Line Singularities by Ridgelets
Axel Obermeier, Philipp Grohs
In [GO15], the authors discussed the existence of numerically feasible solvers for advection equations that run in optimal computational complexity. In this paper, we complete the…
Reconstructing real-valued functions from unsigned coefficients with respect to wavelet and other frames
Rima Alaifari, Ingrid Daubechies, Philipp Grohs +1
In this paper we consider the following problem of phase retrieval: Given a collection of real-valued band-limited functions that consti…