相关论文: Phase retrieval with a multivariate Von Mises prio…

Several deep learning methods for phase retrieval exist, but most of them fail on realistic data without precise support information. We propose a novel method based on single-instance deep generative prior that works well on complex-valued…

This article discusses a generalization of the 1-dimensional multi-reference alignment problem. The goal is to recover a hidden signal from many noisy observations, where each noisy observation includes a random translation and random…

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, a novel Bayesian nonparametric test for assessing multivariate normal models is presented. While there are extensive frequentist and graphical methods for testing multivariate normality, it is challenging to find Bayesian…

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…

The Phase Retrieval problem is dealt with for the challenging case where just a single set of (phaseless) radiated field data is available. In particular, even still emulating the solution of crosswords puzzles, we provide decisive…

In this paper we tackle the problem of recovering the phase of complex linear measurements when only magnitude information is available and we control the input. We are motivated by the recent development of dedicated optics-based hardware…

In this work we develop an algorithm for signal reconstruction from the magnitude of its Fourier transform in a situation where some (non-zero) parts of the sought signal are known. Although our method does not assume that the known part…

We propose a method to restore and to segment simultaneously images degraded by a known point spread function (PSF) and additive white noise. For this purpose, we propose a joint Bayesian estimation framework, where a family of…

We explicitly give a frame of cardinality $5n-6$ such that every signal in $\mathbb{C}^n$ can be recovered up to a phase from its associated intensity measurements via the PhaseLift approach. Furthermore, we give explicit linear…

We consider the problem of finding a low rank symmetric matrix satisfying a system of linear equations, as appears in phase retrieval. In particular, we solve the gauge dual formulation, but use a fast approximation of the spectral…

Phase retrieval aims at recovering a complex-valued signal from magnitude-only measurements, which attracts much attention since it has numerous applications in many disciplines. However, phase recovery involves solving a system of…

Generally, phase retrieval problem can be viewed as the reconstruction of a function/signal from only the magnitude of the linear measurements. These measurements can be, for example, the Fourier transform of the density function.…

Consider a scenario in which an unknown signal is transformed by a known linear operator, and then the pointwise absolute value of the unknown output function is reported. This scenario appears in several applications, and the goal is to…

"Phase retrieval" refers to the recovery of signals from the magnitudes (and not the phases) of linear measurements. While there has been a recent explosion in development of phase retrieval methods, the lack of a common interface has made…

Phaseless super-resolution is the problem of recovering an unknown signal from measurements of the magnitudes of the low frequency Fourier transform of the signal. This problem arises in applications where measuring the phase, and making…

PhaseLift is a noted convex optimization technique for phase retrieval that can recover a signal exactly from amplitude measurements only, with high probability. Conventional PhaseLift requires a relatively large number of samples that…

Phase diversity is a widefield aberration correction method that uses multiple images to estimate the phase aberration at the pupil plane of an imaging system by solving an optimization problem. This estimated aberration can then be used to…

We consider a plane wave, a radiation solution, and the sum of these solutions (total solution) for the Helmholtz equation in an exterior region in $\mathbb{R}^d,$ $d\geq 2$. In this region, we consider a hyperplane $X$ with sufficiently…

In this paper, we consider the generalized phase retrieval from affine measurements. This problem aims to recover signals ${\mathbf x} \in {\mathbb F}^d$ from the affine measurements $y_j=\norm{M_j^*\vx +{\mathbb b}_j}^2,\; j=1,\ldots,m,$…