The problem of phase retrieval, ie, the recovery of a function given the magnitude of its
Fourier transform, arises in various fields of science and engineering, including electron …

Contents Introduction................................................... 264Classic Approaches................................
........... 265 Recent Approaches........................................... 266Sparse Phase …

Spectral methods have emerged as a simple yet surprisingly effective approach for
extracting information from massive, noisy and incomplete data. In a nutshell, spectral …

We consider a family of algorithms that successively sample and minimize simple stochastic
models of the objective function. We show that under reasonable conditions on …

This paper presents a new algorithm, termed truncated amplitude flow (TAF), to recover an
unknown vector x from a system of quadratic equations of the form yi=|< ai, x>| 2, where ai's …

Phase retrieval problems involve solving linear equations, but with missing sign (or phase,
for complex numbers) information. Over the last two decades, a popular generic empirical …

This paper is concerned with finding a solution x to a quadratic system of equations yi=|< ai,
x>|^ 2, i= 1, 2,..., m. We prove that it is possible to solve unstructured quadratic systems in n …

This paper considers the question of recovering the phase of an object from intensity-only
measurements, a problem which naturally appears in X-ray crystallography and related …

We consider the fundamental problem of solving quadratic systems of equations in, and is
unknown. We propose a novel method, which starts with an initial guess computed by …

Recent advances in convex optimization have led to new strides in the phase retrieval
problem over finite-dimensional vector spaces. However, certain fundamental questions …