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Related papers: Phase Retrieval via Smooth Amplitude Flow

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This paper considers the robust phase retrieval, which can be cast as a nonsmooth and nonconvex composite optimization problem. We propose two first-order algorithms with adaptive step sizes: the subgradient algorithm (AdaSubGrad) and the…

Optimization and Control · Mathematics 2026-02-10 Zhong Zheng , Necdet Serhat Aybat , Shiqian Ma , Lingzhou Xue

This paper investigates the sparse phase retrieval problem, which aims to recover a sparse signal from a system of quadratic measurements. In this work, we propose a novel non-convex algorithm, termed Gradient Hard Thresholding Pursuit…

Numerical Analysis · Mathematics 2025-02-18 Licheng Dai , Xiliang Lu , Juntao You

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

Phase retrieval aims at reconstructing unknown signals from magnitude measurements of linear mixtures. In this paper, we consider the phase retrieval with dictionary learning problem, which includes an additional prior information that the…

Signal Processing · Electrical Eng. & Systems 2023-01-24 Tianyi Liu , Andreas M. Tillmann , Yang Yang , Yonina C. Eldar , Marius Pesavento

This paper focuses on stochastic proximal gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer and convex constraints. To the best of our knowledge we present the first non-asymptotic…

Optimization and Control · Mathematics 2019-05-27 Michael R. Metel , Akiko Takeda

In this paper, we tackle the compressive phase retrieval problem in the presence of noise. The noisy compressive phase retrieval problem is to recover a $K$-sparse complex signal $s \in \mathbb{C}^n$, from a set of $m$ noisy quadratic…

Information Theory · Computer Science 2016-06-03 Dong Yin , Kangwook Lee , Ramtin Pedarsani , Kannan Ramchandran

Most methods tackling the phase retrieval problem of magnitude-only antenna measurements suffer from unrealistic sampling requirements, from unfeasible computational complexities, and, most severely, from the lacking reliability of…

Signal Processing · Electrical Eng. & Systems 2022-02-01 Alexander Paulus , Josef Knapp , Jonas Kornprobst , Thomas F. Eibert

The problem of signal recovery from its Fourier transform magnitude is of paramount importance in various fields of engineering and has been around for over 100 years. Due to the absence of phase information, some form of additional…

Information Theory · Computer Science 2015-07-02 Kishore Jaganathan , Samet Oymak , Babak Hassibi

Sparse signals can be recovered from a reduced set of samples by using compressive sensing algorithms. In common methods the signal is recovered in the sparse domain. A method for the reconstruction of sparse signal which reconstructs the…

Information Theory · Computer Science 2015-04-28 Ljubisa Stankovic , Milos Dakovic

Sparse signal recovery based on nonconvex and nonsmooth optimization problems has significant applications and demonstrates superior performance in signal processing and machine learning. This work deals with a scale-invariant…

Optimization and Control · Mathematics 2025-09-29 Lang Yu , Nanjing Huang

Sparse phase retrieval plays an important role in many fields of applied science and thus attracts lots of attention. In this paper, we propose a \underline{sto}chastic alte\underline{r}nating \underline{m}inimizing method for…

Machine Learning · Statistics 2019-06-17 Jianfeng Cai , Yuling Jiao , Xiliang Lu , Juntao You

Analyzing unsteady fluid flows often requires access to the full distribution of possible temporal states, yet conventional PDE solvers are computationally prohibitive and learned time-stepping surrogates quickly accumulate error over long…

Computational Engineering, Finance, and Science · Computer Science 2026-04-14 Mario Lino , Nils Thuerey

If the phase retrieval problem can be solved by a method similar to that of solving a system of linear equations under the context of FFT, the time complexity of computer based phase retrieval algorithm would be reduced. Here I present such…

Numerical Analysis · Mathematics 2013-05-20 Yuan Sun

Phase retrieval problem has been studied in various applications. It is an inverse problem without the standard uniqueness guarantee. To make complete theoretical analyses and devise efficient algorithms to recover the signal is…

Information Theory · Computer Science 2019-05-22 Ziyang Yuan , Hongxia Wang

This paper proposes a new framework to regularize the highly ill-posed and non-linear phase retrieval problem through deep generative priors using simple gradient descent algorithm. We experimentally show effectiveness of proposed algorithm…

Machine Learning · Computer Science 2018-08-20 Fahad Shamshad , Ali Ahmed

This paper deals with finding an $n$-dimensional solution $x$ to a system of quadratic equations of the form $y_i=|\langle{a}_i,x\rangle|^2$ for $1\le i \le m$, which is also known as phase retrieval and is NP-hard in general. We put forth…

Optimization and Control · Mathematics 2017-05-31 Gang Wang , Georgios B. Giannakis , Yousef Saad , Jie Chen

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…

Information Theory · Computer Science 2017-11-08 Tamir Bendory , Robert Beinert , Yonina C. Eldar

We recover the higher order terms for the acoustic wave equation from measurements of the modulus of the solution. The recovery of these coefficients is reduced to a question of stability for inverting a Hamiltonian flow transform, not the…

Analysis of PDEs · Mathematics 2016-07-14 Joonas Ilmavirta , Alden Waters

We propose an accelerated forward-backward method with fast convergence rate for finding a minimizer of a decomposable nonsmooth convex function over a closed convex set, and name it smoothing accelerated proximal gradient (SAPG) algorithm.…

Optimization and Control · Mathematics 2021-10-05 Wei Bian , Fan Wu

The main aim of this paper is to study quaternion phase retrieval (QPR), i.e., the recovery of quaternion signal from the magnitude of quaternion linear measurements. We show that all $d$-dimensional quaternion signals can be reconstructed…

Signal Processing · Electrical Eng. & Systems 2023-07-25 Junren Chen , Michael K. Ng