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 …

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 …

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 …

We consider the problem of phase retrieval, namely, recovery of a signal from the magnitude
of its Fourier transform, or of any other linear transform. Due to the loss of Fourier phase …

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

In phase retrieval, the goal is to recover a signal x∈ CN from the magnitudes of linear
measurements Ax∈ C M. While recent theory has established that M≈ 4N intensity …

Recovering structured models (eg, sparse or group-sparse vectors, low-rank matrices) given
a few linear observations have been well-studied recently. In various applications in signal …

Statistical inference and information processing of high-dimensional data often require an
efficient and accurate estimation of their second-order statistics. With rapidly changing data …