Phase retrieval consists in the recovery of a complex-valued signal from intensity-only
measurements. As it pervades a broad variety of applications, many researchers have …

Phase retrieval, ie the problem of recovering a function from the squared magnitude of its
Fourier transform, arises in many applications, such as X-ray crystallography, diffraction …

The problem of phase retrieval, ie, the problem of recovering a function from the magnitudes
of its Fourier transform, naturally arises in various fields of physics, such as astronomy …

The main result of this paper states that phase retrieval in infinite-dimensional Hilbert spaces
is never uniformly stable, in sharp contrast to the finite-dimensional setting in which phase …

Given a real inner product space V and a group G of linear isometries, we construct a family
of G-invariant real-valued functions on V that we call max filters. In the case where V= R d …

Quantum state tomography (QST) refers to any method that allows one to reconstruct the
accurate representation of a quantum system based on data obtainable from an experiment …

In this paper, we develop a framework of generalized phase retrieval in which one aims to
reconstruct a vector x in R d or C d through quadratic samples x⁎ A 1 x,…, x⁎ AN x. The …

We study identifiability for bilinear inverse problems under sparsity and subspace
constraints. We show that, up to a global scaling ambiguity, almost all such maps are …

Given a real inner product space V and a group G of linear isometries, max filtering offers a
rich class of G-invariant maps. In this paper, we identify nearly sharp conditions under which …

The paper presents several results that address a fundamental question in low-rank matrix
recovery: how many measurements are needed to recover low-rank matrices? We begin by …