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Related papers: Phase Transitions in Phase Retrieval

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In this paper, we provide a detailed overview of the models used for information retrieval in the first and second stages of the typical processing chain. We discuss the current state-of-the-art models, including methods based on terms,…

Information Retrieval · Computer Science 2024-02-16 Kailash A. Hambarde , Hugo Proenca

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…

Image and Video Processing · Electrical Eng. & Systems 2020-12-02 Albert Fannjiang , Thomas Strohmer

Fourier phase retrieval is a classical problem that deals with the recovery of an image from the amplitude measurements of its Fourier coefficients. Conventional methods solve this problem via iterative (alternating) minimization by…

Image and Video Processing · Electrical Eng. & Systems 2020-07-30 Rakib Hyder , Zikui Cai , M. Salman Asif

Phase retrieval deals with the estimation of complex-valued signals solely from the magnitudes of linear measurements. While there has been a recent explosion in the development of phase retrieval algorithms, the lack of a common interface…

Optimization and Control · Mathematics 2017-12-01 Rohan Chandra , Ziyuan Zhong , Justin Hontz , Val McCulloch , Christoph Studer , Tom Goldstein

In this paper we consider the nonlinear inverse problem of phase retrieval in the context of dynamical sampling. Where phase retrieval deals with the recovery of signals & images from phaseless measurements, dynamical sampling was…

Numerical Analysis · Mathematics 2021-02-02 Robert Beinert , Marzieh Hasannasab

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,…

Functional Analysis · Mathematics 2020-02-17 Philipp Grohs , Sarah Koppensteiner , Martin Rathmair

We consider the phase retrieval problem for signals that belong to a union of subspaces. We assume that amplitude measurements of the signal of length $n$ are observed after passing it through a random $m \times n$ measurement matrix. We…

Information Theory · Computer Science 2018-07-18 M. Salman Asif , Chinmay Hegde

Phase retrieval is an inverse problem that, on one hand, is crucial in many applications across imaging and physics, and, on the other hand, leads to deep research questions in theoretical signal processing and applied harmonic analysis.…

We study the convolutional phase retrieval problem, of recovering an unknown signal $\mathbf x \in \mathbb C^n $ from $m$ measurements consisting of the magnitude of its cyclic convolution with a given kernel $\mathbf a \in \mathbb C^m $.…

Computation · Statistics 2019-10-08 Qing Qu , Yuqian Zhang , Yonina C. Eldar , John Wright

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.…

Signal Processing · Electrical Eng. & Systems 2020-03-11 Naveed Naimipour , Shahin Khobahi , Mojtaba Soltanalian

In many applications, signals are measured according to a linear process, but the phases of these measurements are often unreliable or not available. To reconstruct the signal, one must perform a process known as phase retrieval. This paper…

Functional Analysis · Mathematics 2013-07-30 Matthew Fickus , Dustin G. Mixon , Aaron A. Nelson , Yang Wang

Considering the ambiguousness of the discrete-time phase retrieval problem to recover a signal from its Fourier intensities, one can ask the question: what additional information about the unknown signal do we need to select the correct…

Numerical Analysis · Mathematics 2020-02-19 Robert Beinert , Gerlind Plonka

Phase retrieval is a prevalent problem in digital signal processing and experimental physics that consists of estimating a complex signal from magnitude measurements. This paper expands the classical phase retrieval framework to electric…

Signal Processing · Electrical Eng. & Systems 2023-05-17 Samuel Talkington , Santiago Grijalva

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…

Information Theory · Computer Science 2017-07-06 Zhiqiang Xu

This paper is concerned with the problem of recovering a structured signal from a relatively small number of corrupted random measurements. Sharp phase transitions have been numerically observed in practice when different convex programming…

Information Theory · Computer Science 2021-01-05 Zhongxing Sun , Wei Cui , Yulong Liu

Phase retrieval has been an attractive but difficult problem rising from physical science, and there has been a gap between state-of-the-art theoretical convergence analyses and the corresponding efficient retrieval methods. Firstly, these…

Information Theory · Computer Science 2017-12-06 Gen Li , Yuchen Jiao , Yuantao Gu

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…

Signal Processing · Electrical Eng. & Systems 2023-08-16 Giada Maria Battaglia , Andrea Francesco Morabito , Roberta Palmeri , Tommaso Isernia

We describe a new algorithm to solve a particular phase retrieval problem, that has wide applications in audio processing: the reconstruction of a function from its scalogram, that is from the modulus of its wavelet transform. It is a…

Optimization and Control · Mathematics 2017-04-11 Irène Waldspurger

Phase retrieval is in general a non-convex and non-linear task and the corresponding algorithms struggle with the issue of local minima. We consider the case where the measurement samples within typically very small and disconnected subsets…

Signal Processing · Electrical Eng. & Systems 2022-06-28 Jonas Kornprobst , Alexander Paulus , Josef Knapp , Thomas F. Eibert

In many areas of imaging science, it is difficult to measure the phase of linear measurements. As such, one often wishes to reconstruct a signal from intensity measurements, that is, perform phase retrieval. In several applications the…

Information Theory · Computer Science 2015-06-16 Afonso S. Bandeira , Dustin G. Mixon