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Quantum correlation, such as entanglement and squeezing have shown to improve phase estimation in interferometric setups on one side, and non-interferometric imaging scheme of amplitude object on the other. In the last case, quantum…

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

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

The recovery of an unknown signal from its linear measurements is a fundamental problem spanning numerous scientific and engineering disciplines. Commonly, prior knowledge suggests that the underlying signal resides within a known algebraic…

Information Theory · Computer Science 2025-06-27 Zhiqiang Xu

Phase retrieval has been an attractive but difficult problem rising from physical science, and there has been a gap between state-of-the-art theoretical convergence analyses and the corresponding efficient retrieval methods. Firstly, these…

Information Theory · Computer Science 2017-12-06 Gen Li , Yuchen Jiao , Yuantao Gu

The aim of this paper is to study the stability of the $\ell_1$ minimization for the compressive phase retrieval and to extend the instance-optimality in compressed sensing to the real phase retrieval setting. We first show that the…

Functional Analysis · Mathematics 2016-01-12 Bing Gao , Yang Wang , Zhiqiang Xu

We propose an intuitive, simple and hardware friendly, yet surprisingly novel and efficient, received signal's angle of arrival (AoA) estimation scheme. Our intuitive, two-phases cross-correlation based scheme relies on a switched beam…

Systems and Control · Computer Science 2014-09-22 Ahmed Badawy , Tamer Khattab , Daniele Trinchero , Tarek El Fouly , Amr Mohamed

Many applications require recovering a ground truth low-rank matrix from noisy observations of the entries, which in practice is typically formulated as a weighted low-rank approximation problem and solved by non-convex optimization…

Machine Learning · Computer Science 2016-12-09 Yuanzhi Li , Yingyu Liang , Andrej Risteski

Phase retrieval is a nonlinear inverse problem that arises in a wide range of imaging modalities, from electron microscopy to Fourier ptychography. In particular, the reconstruction is facilitated when the sensing matrix is i.i.d. random,…

Phase noise correction is crucial to exploit full advantage of orthogonal frequency division multiplexing (OFDM) in modern high-data-rate communications. OFDM channel estimation with simultaneous phase noise compensation has therefore drawn…

Information Theory · Computer Science 2017-04-25 Zhongju Wang , Prabhu Babu , Daniel P. Palomar

This paper considers the problem of recovering a $k$-sparse, $N$-dimensional complex signal from Fourier magnitude measurements. It proposes a Fourier optics setup such that signal recovery up to a global phase factor is possible with very…

Information Theory · Computer Science 2014-10-28 Çağkan Yapar , Volker Pohl , Holger Boche

We report on progress in algorithms for iterative phase retrieval. The theory of convex optimization is used to develop and to gain insight into counterparts for the nonconvex problem of phase retrieval. We propose a relaxation of averaged…

Optimization and Control · Mathematics 2009-11-10 D. Russell Luke

We consider the problem of reconstructing a low rank matrix from a subset of its entries and analyze two variants of the so-called Alternating Minimization algorithm, which has been proposed in the past. We establish that when the…

Machine Learning · Statistics 2016-09-21 David Gamarnik , Sidhant Misra

Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still…

Machine Learning · Computer Science 2014-05-15 Moritz Hardt

This contribution proposes a two stage strategy to allow for phase retrieval in state of the art sub-Nyquist sampling schemes for sparse multiband signals. The proposed strategy is based on data acquisition via modulated wideband converters…

Information Theory · Computer Science 2015-09-29 Çağkan Yapar , Volker Pohl , Holger Boche

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

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

We consider the problem of reconstructing two signals from the autocorrelation and cross-correlation measurements. This inverse problem is a fundamental one in signal processing, and arises in many applications, including phase retrieval…

Information Theory · Computer Science 2016-10-11 Kishore Jaganathan , Babak Hassibi

The classical alternating minimization (or projection) algorithm has been successful in the context of solving optimization problems over two variables. The iterative nature and simplicity of the algorithm has led to its application to many…

Information Theory · Computer Science 2010-08-24 Urs Niesen , Devavrat Shah , Gregory Wornell

An adaptive iterative decision multi-feedback detection algorithm with constellation constraints is proposed for multiuser multi-antenna systems. An enhanced detection and interference cancellation is performed by introducing multiple…

Information Theory · Computer Science 2013-04-24 Peng Li , Jingjing Liu , Rodrigo C. de Lamare