Related papers: Phase retrieval in infinite-dimensional Hilbert sp…
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 Gabor phase retrieval problem, i.e., the problem of…
In the literature, for semidynamical systems in infinite dimensional phase spaces, different topological structures are used (Hilbert, Banach, Sobolev, locally convex, Hausdorf topology etc.). That is because there are neither set rules nor…
Phase retrieval problems in antenna measurements arise when a reference phase cannot be provided to all measurement locations. Phase retrieval algorithms require sufficiently many independent measurement samples of the radiated fields to be…
Examples are constructed of infinite-dimensional subspaces $V\subset L^2(\mu)$ with the property that for any $f,g\in V$, if $|f|$ is approximately equal to $|g|$ with respect to the $L^2$ norm, then there exists a unimodular scalar $z$…
Deep generative models have become a standard for modeling priors for inverse problems, going beyond classical sparsity-based methods. However, existing theoretical guarantees are mostly confined to finite-dimensional vector spaces,…
Phase retrieval is to recover the signals from phaseless measurements which is raised in many areas. A fundamental problem in phase retrieval is to determine the minimal measurement number $m$ so that one can recover $d$-dimensional signals…
We study nonlinear determination problems in Hilbert spaces in which inner products are observed up to prescribed rotations in the complex plane. Given a Hilbert space $H$ and a subset $\Theta$ of the unit circle $\mathbb{T}$, we say that a…
Phase retrieval has been an attractive but difficult problem rising from physical science, and there has been a gap between state-of-the-art theoretical convergence analyses and the corresponding efficient retrieval methods. Firstly, these…
In this paper, we analyze the discrete inf-sup condition and related error estimates for a modified Hilbert transformation as used in the space-time discretization of time-dependent partial differential equations. It turns out that the…
In this letter, by regarding finite-time stability as an inverse problem, we reveal the essence of finite-time stability and fixed-time stability. Some necessary and sufficient conditions are given. As application, we give a new approach…
In many applications, signals are measured according to a linear process, but the phases of these measurements are often unreliable or not available. To reconstruct the signal, one must perform a process known as phase retrieval. This paper…
In the last five decades, iterative phase retrieval methods draw large amount of interest across the research community as a non-interferometric approach to recover quantitative phase distributions from one (or more) intensity measurement.…
As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…
Gabor phase retrieval for signals has attracted considerable attention in recent years. For the more general short-time linear canonical transform (STLCT), which arises naturally in optical systems and canonical time--frequency analysis,…
In many signal processing problems arising in practical applications, we wish to reconstruct an unknown signal from its phaseless measurements with respect to a frame. This inverse problem is known as the phase retrieval problem. For each…
In this paper, we discuss some limitations of the modified equations approach as a tool for stability analysis for a class of explicit linear schemes to scalar partial derivative equations. We show that the infinite series obtained by…
Phase retrieval is a nonlinear inverse problem that arises in a wide range of imaging modalities, from electron microscopy to Fourier ptychography. In particular, the reconstruction is facilitated when the sensing matrix is i.i.d. random,…
Iterative algorithms with feedback are amongst the most powerful and versatile optimization methods for phase retrieval. Among these, the hybrid input-output algorithm has demonstrated practical solutions to giga-element nonlinear phase…
The generalized phase retrieval problem over compact groups aims to recover a set of matrices -- representing an unknown signal -- from their associated Gram matrices. This framework generalizes the classical phase retrieval problem, which…
The ill-posed problem of phase retrieval in optics, using one or more intensity measurements, has a multitude of applications using electromagnetic or matter waves. Many phase retrieval algorithms are computed on pixel arrays using discrete…