Related papers: Phase Retrieval Versus Phaseless Reconstruction

In this manuscript we demonstrate a method to reconstruct the wavefront of focused beams from a measured diffraction pattern behind a diffracting mask in real-time. The phase problem is solved by means of a neural network, which is trained…

Phase retrieval refers to algorithmic methods for recovering a signal from its phaseless measurements. Local search algorithms that work directly on the non-convex formulation of the problem have been very popular recently. Due to the…

While characterization of coherent wavefields is essential to laser, x-ray and electron imaging, sensors measure the squared magnitude of the field, rather than the field itself. Holography or phase retrieval must be used to characterize…

Suppose we wish to recover a signal x in C^n from m intensity measurements of the form |<x,z_i>|^2, i = 1, 2,..., m; that is, from data in which phase information is missing. We prove that if the vectors z_i are sampled independently and…

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,…

In this paper, we study phase retrievable sequences and give a characterization of phase retrievability of a sequence of bounded linear operators on a Hilbert space $H$; in particular, for $H=\ell_2^d(\Bbb{C})$. We also give several…

Tomography is an imaging technique that works by reconstructing a scene from acquired data in the form of line integrals of the imaging domain. A fundamental underlying assumption in the reconstruction procedure is the precise alignment of…

We present a novel approach for recovery of the directional connectivity of a small oscillator network by means of the phase dynamics reconstruction from multivariate time series data. The main idea is to use a triplet analysis instead of…

Phase retrieval refers to the problem of recovering some signal (which is often modelled as an element of a Hilbert space) from phaseless measurements. It has been shown that in the deterministic setting phase retrieval from frame…

We propose a reliable direct imaging method based on the reverse time migration for finding extended obstacles with phaseless total field data. We prove that the imaging resolution of the method is essentially the same as the imaging…

We consider the problem of reconstructing a function $f\in L^2(\mathbb{R})$ given phase-less samples of its Gabor transform, which is defined by $$\mathcal{G} f(x,\omega) := 2^{\frac14} \int_{\mathbb{R}} f(t) e^{-\pi (t-x)^2} e^{-2\pi i y…

We introduce an efficient method for the reconstruction of the correlation between a compressively measured image and a phase-only filter. The proposed method is based on two properties of phase-only filtering: such filtering is a unitary…

Phase retrieval problems in antenna measurements arise when a reference phase cannot be provided to all measurement locations. Phase retrieval algorithms require sufficiently many independent measurement samples of the radiated fields to be…

We propose a new algorithm to learn a dictionary for reconstructing and sparsely encoding signals from measurements without phase. Specifically, we consider the task of estimating a two-dimensional image from squared-magnitude measurements…

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…

A linear and thus convex phase retrieval algorithm for the application in phaseless near-field far-field transformations is presented. The formulation exploits locally known phase relations among sets of measurement samples, which can in…

A complex frame is a collection of vectors that span $\mathbb{C}^M$ and define measurements, called intensity measurements, on vectors in $\mathbb{C}^M$. In purely mathematical terms, the problem of phase retrieval is to recover a complex…

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…

A randomized Kaczmarz method was recently proposed for phase retrieval, which has been shown numerically to exhibit empirical performance over other state-of-the-art phase retrieval algorithms both in terms of the sampling complexity and in…

Phaseless reconstruction from space-time samples is a nonlinear problem of recovering a function $x$ in a Hilbert space $\mathcal{H}$ from the modulus of linear measurements $\{\lvert \langle x, \phi_i\rangle \rvert$, $ \ldots$, $\lvert…