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We propose a robust and efficient approach to the problem of compressive phase retrieval in which the goal is to reconstruct a sparse vector from the magnitude of a number of its linear measurements. The proposed framework relies on…

Information Theory · Computer Science 2015-10-28 Sohail Bahmani , Justin Romberg

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 to recover the phase information of a signal from the…

Information Theory · Computer Science 2019-10-02 Gilles Baechler , Miranda Kreković , Juri Ranieri , Amina Chebira , Yue M. Lu , Martin Vetterli

High-throughput computational imaging requires efficient processing algorithms to retrieve multi-dimensional and multi-scale information. In computational phase imaging, phase retrieval (PR) is required to reconstruct both amplitude and…

Image and Video Processing · Electrical Eng. & Systems 2021-09-15 Xuyang Chang , Liheng Bian , Jun Zhang

We consider the problem of recovering a $K$-sparse complex signal $x$ from $m$ intensity measurements. We propose the PhaseCode algorithm, and show that in the noiseless case, PhaseCode can recover an arbitrarily-close-to-one fraction of…

Information Theory · Computer Science 2017-04-03 Ramtin Pedarsani , Dong Yin , Kangwook Lee , Kannan Ramchandran

We study the problem of recovering the phase from magnitude measurements; specifically, we wish to reconstruct a complex-valued signal x of C^n about which we have phaseless samples of the form y_r = |< a_r,x >|^2, r = 1,2,...,m (knowledge…

Information Theory · Computer Science 2016-11-17 Emmanuel Candes , Xiaodong Li , Mahdi Soltanolkotabi

On-chip holographic video is a convenient way to monitor biological samples simultaneously at high spatial resolution and over a wide field-of-view. However, due to the limited readout rate of digital detector arrays, one often faces a…

Optics · Physics 2016-12-08 Donghun Ryu , Zihao Wang , Kuan He , Roarke Horstmeyer , Oliver Cossairt

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

Given a linear system in a real or complex domain, linear regression aims to recover the model parameters from a set of observations. Recent studies in compressive sensing have successfully shown that under certain conditions, a linear…

Statistics Theory · Mathematics 2016-11-15 Henrik Ohlsson , Allen Y. Yang , Roy Dong , S. Shankar Sastry

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

Hypercomplex signal processing (HSP) offers powerful tools for analyzing and processing multidimensional signals by explicitly exploiting inter-dimensional correlations through Clifford algebra. In recent years, hypercomplex formulations of…

Signal Processing · Electrical Eng. & Systems 2026-03-02 Kumar Vijay Mishra , Henry Arguello , Brian M. Sadler

We consider the phase retrieval problem of reconstructing a $n$-dimensional real or complex signal $\mathbf{X}^{\star}$ from $m$ (possibly noisy) observations $Y_\mu = | \sum_{i=1}^n \Phi_{\mu i} X^{\star}_i/\sqrt{n}|$, for a large class of…

Statistics Theory · Mathematics 2021-02-18 Antoine Maillard , Bruno Loureiro , Florent Krzakala , Lenka Zdeborová

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

We study the low-rank phase retrieval problem, where the objective is to recover a sequence of signals (typically images) given the magnitude of linear measurements of those signals. Existing solutions involve recovering a matrix…

Image and Video Processing · Electrical Eng. & Systems 2022-02-18 Soo Min Kwon , Xin Li , Anand D. Sarwate

Compressive phase retrieval is a popular variant of the standard compressive sensing problem in which the measurements only contain magnitude information. In this paper, motivated by recent advances in deep generative models, we provide…

Machine Learning · Statistics 2021-10-19 Zhaoqiang Liu , Subhroshekhar Ghosh , Jonathan Scarlett

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

Compressed sensing investigates the recovery of sparse signals from linear measurements. But often, in a wide range of applications, one is given only the absolute values (squared) of the linear measurements. Recovering such signals (not…

Functional Analysis · Mathematics 2015-09-29 Irena Bojarovska , Axel Flinth

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

We analyze continuous-time mirror descent applied to sparse phase retrieval, which is the problem of recovering sparse signals from a set of magnitude-only measurements. We apply mirror descent to the unconstrained empirical risk…

Machine Learning · Statistics 2020-10-21 Fan Wu , Patrick Rebeschini

We explore a fundamental problem of super-resolving a signal of interest from a few measurements of its low-pass magnitudes. We propose a 2-stage tractable algorithm that, in the absence of noise, admits perfect super-resolution of an…

Information Theory · Computer Science 2014-03-10 Yuxin Chen , Yonina C. Eldar , Andrea J. Goldsmith

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