相关论文: Phase retrieval for solutions of the Schr{\"o}ding…
The purpose of this article is to discuss recent advances in the growing field of phase retrieval, and to publicize open problems that we believe will be of interest to mathematicians in general, and algebraists in particular.
This paper discusses the connection between the phase retrieval problem and permutation invariant embeddings. We show that the real phase retrieval problem for $\mathbb{R}^d/O(1)$ is equivalent to Euclidean embeddings of the quotient space…
If the phase retrieval problem can be solved by a method similar to that of solving a system of linear equations under the context of FFT, the time complexity of computer based phase retrieval algorithm would be reduced. Here I present such…
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 problem of phase retrieval is revisited and studied from a fresh perspective. In particular, we establish a connection between the phase retrieval problem and the sensor network localization problem, which allows us to utilize the vast…
Phase retrieval, i.e., the problem of recovering a function from the squared magnitude of its Fourier transform, arises in many applications such as X-ray crystallography, diffraction imaging, optics, quantum mechanics, and astronomy. This…
The problem of recovering a signal from its phaseless Fourier transform measurements, called Fourier phase retrieval, arises in many applications in engineering and science. Fourier phase retrieval poses fundamental theoretical and…
This review article provides a contemporary overview of phase retrieval in optical imaging, linking the relevant optical physics to the information processing methods and algorithms. Its purpose is to describe the current state of the art…
Phase retrieval aims to recover a signal from magnitude or power spectra measurements. It is often addressed by considering a minimization problem involving a quadratic cost function. We propose a different formulation based on Bregman…
In this paper we consider the phase retrieval problem for Herglotz functions, that is, solutions of the Helmholtz equation $\Delta u+\lambda^2u=0$ on domains $\Omega\subset\mathbb{R}^d$, $d\geq2$. In dimension $d=2$, if $u,v$ are two such…
We consider the problem of recovering a spatially-localized cubic nonlinearity in a nonlinear Schr\"odinger equation in dimensions two and three. We prove that solutions with data given by small-amplitude wave packets accrue a nonlinear…
Phase retrieval consists in the recovery of a complex-valued signal from intensity-only measurements. As it pervades a broad variety of applications, many researchers have striven to develop phase-retrieval algorithms. Classical approaches…
The wave equation in quantum mechanics and its general solution in the phase space are obtained.
Phase retrieval is to recover the signals from phaseless measurements which is raised in many areas. A fundamental problem in phase retrieval is to determine the minimal measurement number $m$ so that one can recover $d$-dimensional signals…
We study the problem of recovering the phase from magnitude measurements; specifically, we wish to reconstruct a complex-valued signal x of C^n about which we have phaseless samples of the form y_r = |< a_r,x >|^2, r = 1,2,...,m (knowledge…
We answer a number of open problems concerning phase retrieval and phase retrieval by projections. In particular, one main theorem classifies phase retrieval by projections via collections of sequences of vectors allowing norm retrieval.…
The paper offers the method of discovering of some class of solutions for the nonlinear Schroedinger equation. An algorithm of constructive solving of the Cauchy periodic problem with a finite-gap initial condition was also obtained.
Several strategies in phase retrieval are unified by an iterative "difference map" constructed from a pair of elementary projections and a single real parameter $\beta$. For the standard application in optics, where the two projections…
A class of generalized Schr\"{o}dinger elliptic problems involving concave-convex and other types of nonlinearities is studied. A reasonable overview about the set of solutions is provided when the parameters involved in the equation assume…
We present the first phase retrieval algorithm guaranteed to solve the multidimensional phase retrieval problem in polynomial arithmetic complexity without prior information. The method successfully terminates in O(N log(N)) operations for…