Ptychography is an enabling microscopy technique for both fundamental and applied
sciences. In the past decade, it has become an indispensable imaging tool in most X-ray …

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 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 …

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 …

Unitary $ k $-designs are finite ensembles of unitary matrices that approximate the Haar
distribution over unitary matrices. Several ensembles are known to be 2-designs, including …

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 …

We study the recovery of Hermitian low rank matrices X∈ C n× n from undersampled
measurements via nuclear norm minimization. We consider the particular scenario where …

We study the problem of recovering a vector $\bx\in\bbR^ n $ from its magnitude
measurements $ y_i=|\langle\ba_i,\bx\rangle|, i= 1,..., m $. Our work is along the line of the …