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 …

The resolution of conventional optical lens systems is always hampered by the diffraction
limit. Recent developments in artificial metamaterials provide new avenues to build …

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

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 …

Low-light-level imaging techniques have application in many diverse fields, ranging from
biological sciences to security. A high-quality digital camera based on a multi-megapixel …

This paper develops a novel framework for phase retrieval, a problem which arises in X-ray
crystallography, diffraction imaging, astronomical imaging, and many other applications. Our …

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 present a technique called white-light diffraction tomography (WDT) for imaging
microscopic transparent objects such as live unlabelled cells. The approach extends …

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 …