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Related papers: Conjugate Phase Retrieval in Paley-Wiener Space

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The problem of recovering a vector from the absolute values of its inner products against a family of measurement vectors has been well studied in mathematics and engineering. A generalization of this phase retrieval problem also exists in…

Functional Analysis · Mathematics 2013-07-19 Jameson Cahill , Peter G. Casazza , Jesse Peterson , Lindsey Woodland

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

This paper develops a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging and many other applications. Our approach combines multiple structured illuminations…

Information Theory · Computer Science 2011-09-21 Emmanuel J. Candes , Yonina Eldar , Thomas Strohmer , Vlad Voroninski

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…

Signal Processing · Electrical Eng. & Systems 2025-11-20 Tal Amir , Tamir Bendory , Nadav Dym , Dan Edidin

Phase retrieval (PR), also sometimes referred to as quadratic sensing, is a problem that occurs in numerous signal and image acquisition domains ranging from optics, X-ray crystallography, Fourier ptychography, sub-diffraction imaging, and…

Machine Learning · Computer Science 2020-06-25 Namrata Vaswani

In this paper, we study phase retrieval under model misspecification and generative priors. In particular, we aim to estimate an $n$-dimensional signal $\mathbf{x}$ from $m$ i.i.d.~realizations of the single index model $y =…

Machine Learning · Statistics 2022-10-12 Zhaoqiang Liu , Xinshao Wang , Jiulong Liu

In a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted. Phase retrieval attempts the recovery of the phase information of a signal from…

Information Theory · Computer Science 2013-09-27 Juri Ranieri , Amina Chebira , Yue M. Lu , Martin Vetterli

In the compressive phase retrieval problem, or phaseless compressed sensing, or compressed sensing from intensity only measurements, the goal is to reconstruct a sparse or approximately $k$-sparse vector $x \in \mathbb{R}^n$ given access to…

Data Structures and Algorithms · Computer Science 2020-03-03 Yi Li , Vasileios Nakos

This paper presents a rigorous theoretical convergence analysis of the Wirtinger Flow (WF) algorithm for Poisson phase retrieval, a fundamental problem in imaging applications. Unlike prior analyses that rely on truncation or additional…

Numerical Analysis · Mathematics 2025-01-14 Bing Gao , Ran Gu , Shigui Ma

In this paper, we consider the problem of phase retrieval, which consists of recovering an $n$-dimensional real vector from the magnitude of its $m$ linear measurements. We propose a mirror descent (or Bregman gradient descent) algorithm…

Optimization and Control · Mathematics 2024-06-21 Jean-Jacques Godeme , Jalal Fadili , Xavier Buet , Myriam Zerrad , Michel Lequime , Claude Amra

Phase retrieval(PR) problem is a kind of ill-condition inverse problem which can be found in various of applications. Utilizing the sparse priority, an algorithm called SWF(Sparse Wirtinger Flow) is proposed in this paper to deal with…

Information Theory · Computer Science 2017-04-12 Ziyang Yuan , Qi Wang , Hongxia Wang

This paper considers the question of recovering the phase of an object from intensity-only measurements, a problem which naturally appears in X-ray crystallography and related disciplines. We study a physically realistic setup where one can…

Information Theory · Computer Science 2013-11-08 Emmanuel Candes , Xiaodong Li , Mahdi Soltanolkotabi

We consider the problem of phase retrieval, i.e. that of solving systems of quadratic equations. A simple variant of the randomized Kaczmarz method was recently proposed for phase retrieval, and it was shown numerically to have a…

Numerical Analysis · Mathematics 2018-01-16 Yan Shuo Tan , Roman Vershynin

The classical problem of phase retrieval arises in various signal acquisition systems. Due to the ill-posed nature of the problem, the solution requires assumptions on the structure of the signal. In the last several years, sparsity and…

Computer Vision and Pattern Recognition · Computer Science 2019-03-08 Rakib Hyder , Viraj Shah , Chinmay Hegde , M. Salman Asif

Reconstructing images from their Fourier magnitude measurements is a problem that often arises in different research areas. This process is also referred to as phase retrieval. In this work, we consider a modified version of the phase…

Image and Video Processing · Electrical Eng. & Systems 2021-10-27 Tobias Uelwer , Nick Rucks , Stefan Harmeling

In this paper, we develop a concrete algorithm for phase retrieval, which we refer to as Gauss-Newton algorithm. In short, this algorithm starts with a good initial estimation, which is obtained by a modified spectral method, and then…

Information Theory · Computer Science 2018-02-12 Bing Gao , Zhiqiang Xu

A pupil plane wavefront reconstruction procedure is proposed based on analysis of a sequence of focal plane images corresponding to a sequence of random pupil plane phase probes. The developed method provides the unique nontrivial solution…

Instrumentation and Methods for Astrophysics · Physics 2018-11-13 Eugene Pluzhnik , Dan Sirbu , Ruslan Belikov , Eduardo Bendek , Vladimir N. Dudinov

Phase-retrieval techniques aim to recover the original signal from just the modulus of its Fourier transform, which is usually much easier to measure than its phase, but the standard iterative techniques tend to fail if only part of the…

Image and Video Processing · Electrical Eng. & Systems 2023-07-06 Giovanni Pellegrini , Jacopo Bertolotti

Phase retrieval(PR) problem is a kind of ill-condition inverse problem which is arising in various of applications. Based on the Wirtinger flow(WF) method, a reweighted Wirtinger flow(RWF) method is proposed to deal with PR problem. RWF…

Information Theory · Computer Science 2017-04-05 Ziyang Yuan , Hongxia Wang

This paper explores the problem of generalized phase retrieval, which involves reconstructing a length-$n$ signal $\bm{x}$ from its $m$ phaseless samples $y_k = \left|\langle \bm{a}_k,\bm{x}\rangle\right|^2$, where $k = 1,2,...,m$, and…

Information Theory · Computer Science 2026-04-16 Jianfeng Cai , Huiping Li , Jiayi Li