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 …

We study the problem of recovering the phase from magnitude measurements; specifically,
we wish to reconstruct a complex-valued signal about which we have phaseless samples of …

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 …

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 …

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 …

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 …