Can we recover a complex signal from its Fourier magnitudes? More generally, given a set
of m measurements, y_k=\left| a _k^* x\right| yk= ak∗ x for k= 1, ..., mk= 1,…, m, is it possible …

Recent years have seen a flurry of activities in designing provably efficient nonconvex
optimization procedures for solving statistical estimation problems. For various problems like …

We consider the recovery of a (real-or complex-valued) signal from magnitude-only
measurements, known as phase retrieval. We formulate phase retrieval as a convex …

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 …

This paper develops a novel algorithm, termed SPARse Truncated Amplitude flow
(SPARTA), to reconstruct a sparse signal from a small number of magnitude-only …

We propose a flexible convex relaxation for the phase retrieval problem that operates in the
natural domain of the signal. Therefore, we avoid the prohibitive computational cost …

We consider the problem of phase retrieval, ie that of solving systems of quadratic
equations. A simple variant of the randomized Kaczmarz method was recently proposed for …

This paper concerns the problem of recovering an unknown but structured signal x∈ ℝ n
from m-quadratic measurements of the form yr=|(ar, x)| 2 for r= 1, 2,..., m. We focus on the …

We consider a popular nonsmooth formulation of the real phase retrieval problem. We show
that under standard statistical assumptions a simple subgradient method converges linearly …

This paper deals with finding an n-dimensional solution x to a system of quadratic equations
of the form yi=|< ai, x>| 2 for 1≤ i≤ m, which is also known as the generalized phase …