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This paper considers phase retrieval from the magnitude of 1D over-sampled Fourier measurements, a classical problem that has challenged researchers in various fields of science and engineering. We show that an optimal vector in a…

Optimization and Control · Mathematics 2016-11-03 Kejun Huang , Yonina C. Eldar , Nicholas D. Sidiropoulos

We study the convolutional phase retrieval problem, of recovering an unknown signal $\mathbf x \in \mathbb C^n $ from $m$ measurements consisting of the magnitude of its cyclic convolution with a given kernel $\mathbf a \in \mathbb C^m $.…

Computation · Statistics 2019-10-08 Qing Qu , Yuqian Zhang , Yonina C. Eldar , John Wright

We consider the problem of phase retrieval, i.e. that of solving systems of quadratic equations. A simple variant of the randomized Kaczmarz method was recently proposed for phase retrieval, and it was shown numerically to have a…

Numerical Analysis · Mathematics 2018-01-16 Yan Shuo Tan , Roman Vershynin

In this paper, we provide a detailed overview of the models used for information retrieval in the first and second stages of the typical processing chain. We discuss the current state-of-the-art models, including methods based on terms,…

Information Retrieval · Computer Science 2024-02-16 Kailash A. Hambarde , Hugo Proenca

This paper is concerned with the inverse source problem of reconstructing an unknown acoustic excitation from phaseless measurements of the radiated fields away at multiple frequencies. It is well known that the non-uniqueness issue is a…

Analysis of PDEs · Mathematics 2018-08-01 Deyue Zhang , Yukun Guo , Jingzhi Li , Hongyu Liu

The phase retrieval problem in the classical setting is to reconstruct real/complex functions from the magnitudes of their Fourier/frame measurements. In this paper, we consider a new phase retrieval paradigm in the…

Functional Analysis · Mathematics 2019-09-06 Yang Chen , Cheng Cheng , Qiyu Sun

We consider a variant of the phase retrieval problem, where vectors are replaced by unitary matrices, i.e., the unknown signal is a unitary matrix U, and the measurements consist of squared inner products |Tr(C*U)|^2 with unitary matrices C…

Quantum Physics · Physics 2018-03-07 Shelby Kimmel , Yi-Kai Liu

One of the most powerful approaches to imaging at the nanometer or subnanometer length scale is coherent diffraction imaging using X-ray sources. For amorphous (non-crystalline) samples, the raw data can be interpreted as the modulus of the…

Numerical Analysis · Mathematics 2020-04-02 Alexander Barnett , Charles L. Epstein , Leslie Greengard , Jeremy Magland

This paper introduces a novel technique for reconstructing the phase of modified spectrograms of audio signals. From the analysis of mixtures of sinusoids we obtain relationships between phases of successive time frames in the…

Sound · Computer Science 2016-05-25 Paul Magron , Roland Badeau , Bertrand David

In the phase retrieval problem, the aim is the recovery of an unknown image from intensity-only measurements such as Fourier intensity. Although there are several solution approaches, solving this problem is challenging due to its nonlinear…

Image and Video Processing · Electrical Eng. & Systems 2025-01-20 Cagatay Isil , Figen S. Oktem

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

Consider the task of recovering an unknown $n$-vector from phaseless linear measurements. This task is the phase retrieval problem. Through the technique of lifting, this nonconvex problem may be convexified into a semidefinite rank-one…

Optimization and Control · Mathematics 2015-02-17 Paul Hand

The generalized phase retrieval problem over compact groups aims to recover a set of matrices -- representing an unknown signal -- from their associated Gram matrices. This framework generalizes the classical phase retrieval problem, which…

Signal Processing · Electrical Eng. & Systems 2025-11-20 Tal Amir , Tamir Bendory , Nadav Dym , Dan Edidin

Real-valued Phase retrieval is a non-convex continuous inference problem, where a high-dimensional signal is to be reconstructed from a dataset of signless linear measurements. Focusing on the noiseless case, we aim to disentangle the two…

Disordered Systems and Neural Networks · Physics 2025-02-07 Davide Straziota , Luca Saglietti

We propose a new algorithm to learn a dictionary for reconstructing and sparsely encoding signals from measurements without phase. Specifically, we consider the task of estimating a two-dimensional image from squared-magnitude measurements…

Optimization and Control · Mathematics 2016-11-23 Andreas M. Tillmann , Yonina C. Eldar , Julien Mairal

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

X-ray propagation-based imaging techniques are well-established at synchrotron radiation and laboratory sources. However, most reconstruction algorithms for such image modalities, also known as phase retrieval algorithms, have been…

Image and Video Processing · Electrical Eng. & Systems 2020-12-16 Max Langer , Yuhe Zhang , Diogo Figueirinhas , Jean-Baptiste Forien , Claire Mouton , Rajmund Mokso , Pablo Villanueva-Perez

We study the Kaczmarz methods for solving systems of quadratic equations, i.e., the generalized phase retrieval problem. The methods extend the Kaczmarz methods for solving systems of linear equations by integrating a phase selection…

Numerical Analysis · Mathematics 2015-09-01 Ke Wei

We prove by means of elementary methods that phase retrieval of complex polynomials p of degree less than N is possible with 4N-4 phaseless Fourier measurements of p and p'. In addition, we provide an associated algorithm and prove that it…

Functional Analysis · Mathematics 2014-03-20 Friedrich Philipp

Fourier Ptychography is a recently proposed imaging technique that yields high-resolution images by computationally transcending the diffraction blur of an optical system. At the crux of this method is the phase retrieval algorithm, which…

Computer Vision and Pattern Recognition · Computer Science 2018-05-10 Lokesh Boominathan , Mayug Maniparambil , Honey Gupta , Rahul Baburajan , Kaushik Mitra