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Related papers: Phase retrieval for sub-Gaussian measurements

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We consider the robust phase retrieval problem of recovering the unknown signal from the magnitude-only measurements, where the measurements can be contaminated by both sparse arbitrary corruption and bounded random noise. We propose a new…

Machine Learning · Statistics 2018-01-08 Jinghui Chen , Lingxiao Wang , Xiao Zhang , Quanquan Gu

Phase retrieval, a nonlinear problem prevalent in imaging applications, has been extensively studied using random models, some of which with i.i.d. sensing matrix components. While these models offer robust reconstruction guarantees, they…

Optics · Physics 2024-09-10 Zhiyuan Hu , Julián Tachella , Michael Unser , Jonathan Dong

We address the problem of signal reconstruction from intensity measurements with respect to a measurement frame. This non-convex inverse problem is known as phase retrieval. The case considered in this paper concerns phaseless measurements…

Functional Analysis · Mathematics 2019-02-13 Goetz E. Pfander , Palina Salanevich

We study the sparse phase retrieval problem, which seeks to recover a sparse signal from a limited set of magnitude-only measurements. In contrast to prevalent sparse phase retrieval algorithms that primarily use first-order methods, we…

Information Theory · Computer Science 2024-03-20 Jian-Feng Cai , Yu Long , Ruixue Wen , Jiaxi Ying

A recently proposed convex formulation of the phase retrieval problem estimates the unknown signal by solving a simple linear program. This new scheme, known as PhaseMax, is computationally efficient compared to standard convex relaxation…

Information Theory · Computer Science 2017-10-17 Oussama Dhifallah , Christos Thrampoulidis , Yue M. Lu

We report an iterative algorithm to retrieve accurate real space information from gas phase ultrafast diffraction measurements with missing data at low momentum transfer. The algorithm operates in a manner similar to phase retrieval…

Chemical Physics · Physics 2026-02-25 Yanwei Xiong , Nikhil Kumar Pachisia , Martin Centurion

In this work we consider the problem of reconstruction of a signal from the magnitude of its Fourier transform, also known as phase retrieval. The problem arises in many areas of astronomy, crystallography, optics, and coherent diffraction…

Optics · Physics 2012-03-22 Eliyahu Osherovich

Sparse modeling is one of the efficient techniques for imaging that allows recovering lost information. In this paper, we present a novel iterative phase-retrieval algorithm using a sparse representation of the object amplitude and phase.…

Computer Vision and Pattern Recognition · Computer Science 2011-08-17 Artem Migukin , Vladimir Katkovnik , Jaakko Astola

Phase retrieval problems involve solving linear equations, but with missing sign (or phase, for complex numbers) information. More than four decades after it was first proposed, the seminal error reduction algorithm of (Gerchberg and Saxton…

Machine Learning · Statistics 2015-06-15 Praneeth Netrapalli , Prateek Jain , Sujay Sanghavi

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

The phase retrieval from multi-frequency intensity (power) observations is considered. The object to be reconstructed is complex-valued. A novel algorithm is presented that accomplishes both the object phase (absolute phase) retrieval and…

Signal Processing · Electrical Eng. & Systems 2018-02-07 Vladimir Katkovnik , Karen Egiazarian

Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…

Optimization and Control · Mathematics 2025-05-30 Jun Fan , Ailing Yan , Xianchao Xiu , Wanquan Liu

We study an approach to solving the phase retrieval problem as it arises in a phase-less imaging modality known as ptychography. In ptychography, small overlapping sections of an unknown sample (or signal, say $x_0\in \mathbb{C}^d$) are…

Numerical Analysis · Mathematics 2019-10-09 Brian Preskitt , Rayan Saab

The paper considers the phase retrieval problem in N-dimensional complex vector spaces. It provides two sets of deterministic measurement vectors which guarantee signal recovery for all signals, excluding only a specific subspace and a…

Information Theory · Computer Science 2014-07-21 Volker Pohl , Fanny Yang , Holger Boche

Signal inpainting is the task of restoring degraded or missing samples in a signal. In this paper we address signal inpainting when Fourier magnitudes are observed. We propose a mathematical formulation of the problem that highlights its…

Signal Processing · Electrical Eng. & Systems 2023-06-23 Louis Bahrman , Marina Krémé , Paul Magron , Antoine Deleforge

Solving quadratic systems of equations in n variables and m measurements of the form $y_i = |a^T_i x|^2$ , $i = 1, ..., m$ and $x \in R^n$ , which is also known as phase retrieval, is a hard nonconvex problem. In the case of standard…

Optimization and Control · Mathematics 2019-05-24 Zhenwei Luo , Ye Zhang

In this paper, we develop a new computational approach which is based on minimizing the difference of two convex functionals (DC) to solve a broader class of phase retrieval problems. The approach splits a standard nonlinear least squares…

Information Theory · Computer Science 2018-10-23 Meng Huang , Ming-Jun Lai , Abraham Varghese , Zhiqiang Xu

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

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

This work examines the multi-view compressive phase retrieval problem in a distributed sensor network, where each sensor device, limited by storage and sensing capabilities, can access only intensity measurements from an unknown part of the…

Information Theory · Computer Science 2025-06-02 Ming-Hsun Yang