39 citations · 215 across the 17 of their papers we have counts for
21 papers
Cheeger's Constant for the Gabor Transform and Ripples
Rima Alaifari, Ben Pineau, Mitchell A. Taylor +1
We discover a new instability mechanism for short-time Fourier transform phase retrieval which yields that for any reasonable window function in any dimension , the local st…
On stability for wave propagation and for linear inverse problems
Rima Alaifari, Giovanni S. Alberti, Tandri Gauksson
Stability is a key property of both forward models and inverse problems, and depends on the norms considered in the relevant function spaces. For instance, stability estimates for…
Multi-Window Approaches for Direct and Stable STFT Phase Retrieval
Rima Alaifari, Yunan Yang
Phase retrieval from phaseless short-time Fourier transform (STFT) measurements is known to be inherently unstable when measurements are taken with respect to a single window. Whil…
Uncovering the limits of uniqueness in sampled Gabor phase retrieval: A dense set of counterexamples in
Rima Alaifari, Francesca Bartolucci, Matthias Wellershoff
Sampled Gabor phase retrieval - the problem of recovering a square-integrable signal from the magnitude of its Gabor transform sampled on a lattice - is a fundamental problem in si…
Representation Equivalent Neural Operators: a Framework for Alias-free Operator Learning
Francesca Bartolucci, Emmanuel de Bézenac, Bogdan Raonić +3
Recently, operator learning, or learning mappings between infinite-dimensional function spaces, has garnered significant attention, notably in relation to learning partial differen…
Unique wavelet sign retrieval from samples without bandlimiting
Rima Alaifari, Francesca Bartolucci, Matthias Wellershoff
We study the problem of recovering a signal from magnitudes of its wavelet frame coefficients when the analyzing wavelet is real-valued. We show that every real-valued signal can b…
Convolutional Neural Operators for robust and accurate learning of PDEs
Bogdan Raonić, Roberto Molinaro, Tim De Ryck +5
Although very successfully used in conventional machine learning, convolution based neural network architectures -- believed to be inconsistent in function space -- have been large…
Localized adversarial artifacts for compressed sensing MRI
Rima Alaifari, Giovanni S. Alberti, Tandri Gauksson
As interest in deep neural networks (DNNs) for image reconstruction tasks grows, their reliability has been called into question (Antun et al., 2020; Gottschling et al., 2020). How…
On the connection between uniqueness from samples and stability in Gabor phase retrieval
Rima Alaifari, Francesca Bartolucci, Stefan Steinerberger +1
Gabor phase retrieval is the problem of reconstructing a signal from only the magnitudes of its Gabor transform. Previous findings suggest a possible link between unique solvabilit…
Phase retrieval from sampled Gabor transform magnitudes: Counterexamples
Rima Alaifari, Matthias Wellershoff
We consider the recovery of square-integrable signals from discrete, equidistant samples of their Gabor transform magnitude and show that, in general, signals can not be recovered…
Phase retrieval of bandlimited functions for the wavelet transform
Rima Alaifari, Francesca Bartolucci, Matthias Wellershoff
We study the recovery of square-integrable signals from the absolute values of their wavelet transforms, also called wavelet phase retrieval. We present a new uniqueness result for…
Uniqueness of STFT phase retrieval for bandlimited functions
Rima Alaifari, Matthias Wellershoff
We consider the problem of phase retrieval from magnitudes of short-time Fourier transform (STFT) measurements. It is well-known that signals are uniquely determined (up to global…
Stability estimates for phase retrieval from discrete Gabor measurements
Rima Alaifari, Matthias Wellershoff
Phase retrieval refers to the problem of recovering some signal (which is often modelled as an element of a Hilbert space) from phaseless measurements. It has been shown that in th…
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…
ADef: an Iterative Algorithm to Construct Adversarial Deformations
Rima Alaifari, Giovanni S. Alberti, Tandri Gauksson
While deep neural networks have proven to be a powerful tool for many recognition and classification tasks, their stability properties are still not well understood. In the past, i…
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…
Stability estimates for the regularized inversion of the truncated Hilbert transform
Rima Alaifari, Michel Defrise, Alexander Katsevich
In limited data computerized tomography, the 2D or 3D problem can be reduced to a family of 1D problems using the differentiated backprojection (DBP) method. Each 1D problem consis…
Asymptotic analysis of the SVD for the truncated Hilbert transform with overlap
Reema Al-Aifari, Michel Defrise, Alexander Katsevich
The truncated Hilbert transform with overlap is an operator that arises in tomographic reconstruction from limited data, more precisely in the method of Differentiated Back-P…
Lower bounds for the truncated Hilbert transform
Rima Alaifari, Lillian B. Pierce, Stefan Steinerberger
Given two intervals , we ask whether it is possible to reconstruct a real-valued function from knowing its Hilbert transform on . Wh…