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 …

In many areas of imaging science, it is difficult to measure the phase of linear
measurements. As such, one often wishes to reconstruct a signal from intensity …

The problem of retrieving phase information from amplitude measurements alone has
appeared in many scientific disciplines over the last century. PhaseLift is a recently …

We collect some recent results that together provide an almost complete answer to the
question stated in the title. For the dimension d= 2 the answer is three. For the dimensions …

Compressed sensing and its extensions have recently triggered interest in randomized
signal acquisition. A key finding is that random measurements provide sparse signal …

In this paper, we investigate an extension of Pauli's phase retrieval problem. The original
problem asks whether a function u is uniquely determined by its modulus| u| and the …

For any finite-dimensional Hilbert space, we construct explicitly five orthonormal bases such
that the corresponding measurements allow for efficient tomography of an arbitrary pure …

We prove two results with regard to reconstruction from magnitudes of frame coefficients (the
so called “phase retrieval problem”). First we show that phase retrievable nonlinear maps …

In this dissertation we discuss three problems characterized by hidden structure or
information. The first part of this thesis focuses on extracting subspace structures from data …

In this paper, we consider the question of finding an as small as possible family of operators
(T j) j∈ J on L 2 (R) that does phase retrieval: every φ is uniquely determined (up to a …