153 citations · 899 across the 45 of their papers we have counts for
26 papers · 1 filter
Phase retrieval in Fock space and perturbation of Liouville sets
Philipp Grohs, Lukas Liehr, Martin Rathmair
We study the determination of functions in Fock space from samples of their absolute value, known as the phase retrieval problem in Fock space. An important finding in this researc…
From completeness of discrete translates to phaseless sampling of the short-time Fourier transform
Philipp Grohs, Lukas Liehr, Irina Shafkulovska
We study the uniqueness problem in short-time Fourier transform phase retrieval by exploring a connection to the completeness problem of discrete translates. Specifically, we prove…
Phaseless sampling on square-root lattices
Philipp Grohs, Lukas Liehr
Due to its appearance in a remarkably wide field of applications, such as audio processing and coherent diffraction imaging, the short-time Fourier transform (STFT) phase retrieval…
Multi-window STFT phase retrieval: lattice uniqueness
Philipp Grohs, Lukas Liehr, Martin Rathmair
Short-time Fourier transform (STFT) phase retrieval refers to the reconstruction of a function from its spectrogram, i.e., the magnitudes of its short-time Fourier transform $V…
Non-uniqueness theory in sampled STFT phase retrieval
Philipp Grohs, Lukas Liehr
The reconstruction of a function from its spectrogram (i.e., the absolute value of its short-time Fourier transform (STFT)) arises as a key problem in several important application…
On foundational discretization barriers in STFT phase retrieval
Philipp Grohs, Lukas Liehr
We prove that there exists no window function and no lattice such that every is determined up to…
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…
Stable Gabor phase retrieval in Gaussian shift-invariant spaces via biorthogonality
Philipp Grohs, Lukas Liehr
We study the phase reconstruction of signals belonging to complex Gaussian shift-invariant spaces from spectrogram measurements where $\mathc…
-stability analysis for Gabor phase retrieval
Philipp Grohs, Martin Rathmair
We consider the problem of reconstructing the missing phase information from spectrogram data with $$ \mathcal{G}f(x,y)=\int_\mathbb{R} f(t) e^{-π(t-x)^2}e^{-2πi…
Phase Transitions in Rate Distortion Theory and Deep Learning
Philipp Grohs, Andreas Klotz, Felix Voigtlaender
Rate distortion theory is concerned with optimally encoding a given signal class using a budget of bits, as . We say that can be compres…
Injectivity of Gabor phase retrieval from lattice measurements
Philipp Grohs, Lukas Liehr
We establish novel uniqueness results for the Gabor phase retrieval problem: if denotes the Gabor transform then every $f \in…
Stable Gabor phase retrieval for multivariate functions
Philipp Grohs, Martin Rathmair
In recent work [P. Grohs and M. Rathmair. Stable Gabor Phase Retrieval and Spectral Clustering. Communications on Pure and Applied Mathematics (2018)] the instabilities of the Gabo…
Phase Retrieval: Uniqueness and Stability
Philipp Grohs, Sarah Koppensteiner, Martin Rathmair
The problem of phase retrieval, i.e., the problem of recovering a function from the magnitudes of its Fourier transform, naturally arises in various fields of physics, such as astr…
DNN Expression Rate Analysis of High-dimensional PDEs: Application to Option Pricing
Dennis Elbrächter, Philipp Grohs, Arnulf Jentzen +1
We analyze approximation rates by deep ReLU networks of a class of multi-variate solutions of Kolmogorov equations which arise in option pricing. Key technical devices are deep ReL…
Gabor phase retrieval is severely ill-posed
Rima Alaifari, Philipp Grohs
The problem of reconstructing a function from the magnitudes of its frame coefficients has recently been shown to be never uniformly stable in infinite-dimensional spaces [5]. This…
Stable Gabor Phase Retrieval and Spectral Clustering
Philipp Grohs, Martin Rathmair
We consider the problem of reconstructing a signal from its spectrogram, i.e., the magnitudes of its Gabor transform $$V_φf (x,y):=\int_{\mathbb{R}}f(t)e^{-π(t-x)^2}e^…
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…
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…
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…
Anisotropic Multiscale Systems on Bounded Domains
Philipp Grohs, Gitta Kutyniok, Jackie Ma +2
We provide a construction of multiscale systems on a bounded domain coined boundary shearlet systems, which satisfy several properties advantageous for appl…
-Molecules
Philipp Grohs, Sandra Keiper, Gitta Kutyniok +1
Within the area of applied harmonic analysis, various multiscale systems such as wavelets, ridgelets, curvelets, and shearlets have been introduced and successfully applied. The ke…
Cartoon Approximation with -Curvelets
Philipp Grohs, Sandra Keiper, Gitta Kutyniok +1
It is well-known that curvelets provide optimal approximations for so-called cartoon images which are defined as piecewise -functions, separated by a singularity curve.…
Intrinsic Localization of Anisotropic Frames II: -Molecules
Philipp Grohs, Stefano Vigogna
This article is a continuation of the recent paper [Grohs, Intrinsic localization of anisotropic frames, ACHA, 2013], where off-diagonal-decay properties (often referred to as 'loc…
Parabolic Molecules
Philipp Grohs, Gitta Kutyniok
Anisotropic decompositions using representation systems based on parabolic scaling such as curvelets or shearlets have recently attracted significantly increased attention due to t…