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Phase retrieval refers to the problem of recovering a high-dimensional vector $\boldsymbol{x} \in \mathbb{C}^N$ from the magnitude of its linear transform $\boldsymbol{z} = A \boldsymbol{x}$, observed through a noisy channel. To improve the…

Computation · Statistics 2024-10-10 Hajime Ueda , Shun Katakami , Masato Okada

Phase retrieval seeks to recover a complex signal from amplitude-only measurements, a challenging nonlinear inverse problem. Current theory and algorithms often ignore signal priors. By contrast, we evaluate here a variety of image priors…

Image and Video Processing · Electrical Eng. & Systems 2025-09-19 Stanislas Ducotterd , Zhiyuan Hu , Michael Unser , Jonathan Dong

In this paper, we develop a framework of generalized phase retrieval in which one aims to reconstruct a vector ${\mathbf x}$ in ${\mathbb R}^d$ or ${\mathbb C}^d$ through quadratic samples ${\mathbf x}^*A_1{\mathbf x}, \dots, {\mathbf…

Information Theory · Computer Science 2016-06-06 Yang Wang , Zhiqiang Xu

Supervised topic models simultaneously model the latent topic structure of large collections of documents and a response variable associated with each document. Existing inference methods are based on variational approximation or Monte…

Machine Learning · Computer Science 2016-02-22 Yong Ren , Yining Wang , Jun Zhu

The phase retrieval problem in the presence of noise aims to recover the signal vector of interest from a set of quadratic measurements with infrequent but arbitrary corruptions, and it plays an important role in many scientific…

Machine Learning · Statistics 2024-09-04 Zhong Zheng , Lingzhou Xue

Phase retrieval arises in various fields of science and engineering and it is well studied in a finite-dimensional setting. In this paper, we consider an infinite-dimensional phase retrieval problem to reconstruct real-valued signals living…

Information Theory · Computer Science 2016-03-07 Yang Chen , Cheng Cheng , Qiyu Sun , Haichao Wang

Phase retrieval has important applications in optical imaging, communications and sensing. Lifting the dimensionality of the problem allows phase retrieval to be approximated as a convex optimization problem in a higher-dimensional space.…

Information Theory · Computer Science 2018-05-09 Sercan O. Arik , Joseph M. Kahn

Traditional phase-shifting interferometry technique cannot be used to measure time-varying phase distributions. But single shot techniques could resolve the problem. Many efforts have been made on the phase retrieval methods from a single…

Instrumentation and Detectors · Physics 2020-03-31 Lifa Hu , Wen Shena , Wenchao Ma , Dongting Hu , Xinyu Liu

Phase retrieval consists in the recovery of an unknown signal from phaseless measurements of its usually complex-valued Fourier transform. Without further assumptions, this problem is notorious to be severe ill posed such that the recovery…

Information Theory · Computer Science 2023-01-19 Robert Beinert , Saghar Rezaei

High-dimensional matrix regression has been studied in various aspects, such as statistical properties, computational efficiency and application to specific instances including multivariate regression, system identification and matrix…

Statistics Theory · Mathematics 2024-03-06 Xin Li , Dongya Wu

This paper considers the problem of sampling and reconstruction of a continuous-time sparse signal without assuming the knowledge of the sampling instants or the sampling rate. This topic has its roots in the problem of recovering multiple…

Information Theory · Computer Science 2017-01-31 Ayush Bhandari , Aurelien Bourquard , Ramesh Raskar

We consider the task of recovering two real or complex $m$-vectors from phaseless Fourier measurements of their circular convolution. Our method is a novel convex relaxation that is based on a lifted matrix recovery formulation that allows…

Information Theory · Computer Science 2019-05-14 Ali Ahmed , Alireza Aghasi , Paul Hand

This paper aims to address the phase retrieval problem from subgaussian measurements with arbitrary noise, with a focus on devising robust and efficient algorithms for solving non-convex problems. To ensure uniqueness of solutions in the…

Optimization and Control · Mathematics 2024-12-11 Haiyang Peng , Deren Han , Linbin Li , Meng Huang

We consider the recovery of a (real- or complex-valued) signal from magnitude-only measurements, known as phase retrieval. We formulate phase retrieval as a convex optimization problem, which we call PhaseMax. Unlike other convex methods…

Information Theory · Computer Science 2018-01-31 Tom Goldstein , Christoph Studer

Phase imaging techniques extract the optical path-length information of a scene, whereas wavefront sensors provide the shape of an optical wavefront. Since these two applications have different technical requirements, they have developed…

Optics · Physics 2018-02-28 F. Soldevila , V. Durán , P. Clemente , J. Lancis , E. Tajahuerce

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…

Machine Learning · Computer Science 2020-02-17 Sidharth Gupta , Rémi Gribonval , Laurent Daudet , Ivan Dokmanić

We study the problem of recovering the underlining sparse signals from clean or noisy phaseless measurements. Due to the sparse prior of signals, we adopt an L0regularized variational model to ensure only a small number of nonzero elements…

Optimization and Control · Mathematics 2016-12-09 Yuping Duan , Chunlin Wu , Zhi-Feng Pang , Huibin Chang

In this work we analyze the problem of phase retrieval from Fourier measurements with random diffraction patterns. To this end, we consider the recently introduced PhaseLift algorithm, which expresses the problem in the language of convex…

Information Theory · Computer Science 2017-01-10 David Gross , Felix Krahmer , Richard Kueng

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.…

Optimization and Control · Mathematics 2019-11-21 Bing Gao , Haixia Liu , Yang Wang

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