Related papers: Phase retrieval by power iterations
Phase retrieval, or the process of recovering phase information in reciprocal space to reconstruct images from measured intensity alone, is the underlying basis to a variety of imaging applications including coherent diffraction imaging…
Given underdetermined measurements of a Positive Semi-Definite (PSD) matrix $X$ of known low rank $K$, we present a new algorithm to estimate $X$ based on recent advances in non-convex optimization schemes. We apply this in particular to…
We consider a phase retrieval problem, where the goal is to reconstruct a $n$-dimensional complex vector from its phaseless scalar products with $m$ sensing vectors, independently sampled from complex normal distributions. We show that,…
To obtain spatial information about an arbitrary object in x-ray structure analysis, the standard method is to measure the intensity in the far field, i.e., the first-order photon correlation function of the coherently scattered x-ray…
The problem of phase retrieval, i.e., the problem of recovering a function from the magnitudes of its Fourier transform, naturally arises in various fields of physics, such as astronomy, radar, speech recognition, quantum mechanics and,…
The classical Kaczmarz iteration and its randomized variants are popular tools for fast inversion of linear overdetermined systems. This method extends naturally to the setting of the phase retrieval problem via substituting at each…
This paper investigates the convergence of the randomized Kaczmarz algorithm for the problem of phase retrieval of complex-valued objects. While this algorithm has been studied for the real-valued case}, its generalization to the…
A new method recovers the phase difference of interfering wavefronts from a pattern of interference fringes, avoiding the phase discontinuity problem. The method relies on the numerical solution of one-dimensional first-order ordinary…
In this paper, we develop a novel phase retrieval approach to reconstruct x-ray differential phase shift induced by an object. A primary advantage of our approach is a higher-order accuracy over that with the conventional linear…
The phase retrieval problem has a long history and is an important problem in many areas of optics. Theoretical understanding of phase retrieval is still limited and fundamental questions such as uniqueness and stability of the recovered…
We demonstrate a new approach to the analysis of extensive multi-energy data. For the case of d + He-4, we produce a phase shift analysis covering for the energy range 3 to 11 MeV. The key idea is the use of iterative perturbative…
We consider the phase retrieval problem, in which the observer wishes to recover a $n$-dimensional real or complex signal $\mathbf{X}^\star$ from the (possibly noisy) observation of $|\mathbf{\Phi} \mathbf{X}^\star|$, in which…
In phase retrieval, the goal is to recover a complex signal from the magnitude of its linear measurements. While many well-known algorithms guarantee deterministic recovery of the unknown signal using i.i.d. random measurement matrices,…
This paper presents a novel approach on solving the phase problem in nuclear magnetic resonance (NMR) diffusion pore imaging, a method, which allows imaging the shape of arbitrary closed pores filled with an NMR-detectable medium for…
The problem of phase retrieval has been intriguing researchers for decades due to its appearance in a wide range of applications. The task of a phase retrieval algorithm is typically to recover a signal from linear phase-less measurements.…
We consider the problem of conjugate phase retrieval in Paley-Wiener space $PW_{\pi}$. The goal of conjugate phase retrieval is to recover a signal $f$ from the magnitudes of linear measurements up to unknown phase factor and unknown…
The problem of recovering a vector from the absolute values of its inner products against a family of measurement vectors has been well studied in mathematics and engineering. A generalization of this phase retrieval problem also exists in…
The coherent radiation emitted by an electron bunch provides a diagnostic signal that can be used to estimate its longitudinal distribution. Commonly only the amplitude of the intensity spectrum can be measured and the associated phase must…
Interferometric methods, renowned for their reliability and precision, play a vital role in phase imaging. Interferometry typically requires high coherence and stability between the measured and the reference beam. The presence of rapid…
We study phase retrieval from magnitude measurements of an unknown signal as an algebraic estimation problem. Indeed, phase retrieval from rank-one and more general linear measurements can be treated in an algebraic way. It is verified that…