Related papers: Phase Retrieval in Hardy Space
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…
A new method for phase recovery from a single two-beam interferogram is presented. Conventional approaches, relying on trigonometric inversion followed by phase unfolding and unwrapping, are hindered by discontinuities typically addressed…
We investigate the uniqueness of short-time Fourier transform phase retrieval problems in $L^2(\mathbb{R})$. In particular, for underlying window functions whose Fourier transform decay faster than any exponential function, we derive…
The ill-posed problem of phase retrieval in optics, using one or more intensity measurements, has a multitude of applications using electromagnetic or matter waves. Many phase retrieval algorithms are computed on pixel arrays using discrete…
We implement numerically formulas of [Isaev, Novikov, arXiv:2107.07882] for finding a compactly supported function $v$ on $\mathbb{R}^d$, $d\geq 1$, from its Fourier transform $\mathcal{F} [v]$ given within the ball $B_r$. For the…
Phase retrieval problems occur in a width range of applications in physics and engineering such as crystallography, astronomy, and laser optics. Common to all of them is the recovery of an unknown signal from the intensity of its Fourier…
In this paper, we focus on the problem of phase retrieval from intensity measurements of the Short-Time Linear Canonical Transform (STLCT). Specifically, we show that the STLCT allows for the unique recovery of any square-integrable…
In recent work [P. Grohs and M. Rathmair. Stable Gabor Phase Retrieval and Spectral Clustering. Communications on Pure and Applied Mathematics (2018)] the instabilities of the Gabor phase retrieval problem, i.e., the problem of…
The generalized phase retrieval problem over compact groups aims to recover a set of matrices -- representing an unknown signal -- from their associated Gram matrices. This framework generalizes the classical phase retrieval problem, which…
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 paper presents a method for reconstructing an acoustic source located in a two-layered medium from multi-frequency phased or phaseless far-field patterns measured on the upper hemisphere. The interface between the two media is assumed…
In signal processing, several applications involve the recovery of a function given noisy modulo samples. The setting considered in this paper is that the samples corrupted by an additive Gaussian noise are wrapped due to the modulo…
We present a variational method for recovering the phase term from the information obtained from phase-shifting methods. First we introduce the new method based on a variational approach and then describe the numerical solution of the…
We consider the inverse problem of recovering a binary function from blurred and noisy data. Such problems arise in many applications, for example image processing and optimal control of PDEs. Our formulation is based on the Mumford-Shah…
Conjugate phase retrieval considers the recovery of a function, up to a unimodular constant and conjugation, from its phaseless measurements. In this paper, we explore the conjugate phase retrieval in a shift-invariant space generated by a…
The reconstruction of spectral functions from Euclidean correlation functions is a well-known, yet ill-posed inverse problem in the fields of many-body and high-energy physics. In this paper, we present a comprehensive investigation of two…
This paper presents some results on a well-known problem in Algebraic Signal Sampling and in other areas of applied mathematics: reconstruction of piecewise-smooth functions from their integral measurements (like moments, Fourier…
Phase retrieval, the problem of recovering lost phase information from measured intensity alone, is an inverse problem that is widely faced in various imaging modalities ranging from astronomy to nanoscale imaging. The current process of…
As a generalization of the standard phase retrieval problem, we seek to reconstruct symmetric rank-1 matrices from inner products with subclasses of positive semidefinite matrices. For such subclasses, we introduce random cubatures for…
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…