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Related papers: Phase retrieval from low-rate samples

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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 phase retrieval is revisited and studied from a fresh perspective. In particular, we establish a connection between the phase retrieval problem and the sensor network localization problem, which allows us to utilize the vast…

Optimization and Control · Mathematics 2018-03-22 Sherry Xue-Ying Ni , Man-Chung Yue , Kam-Fung Cheung , Anthony Man-Cho So

In this paper we consider the nonlinear inverse problem of phase retrieval in the context of dynamical sampling. Where phase retrieval deals with the recovery of signals & images from phaseless measurements, dynamical sampling was…

Numerical Analysis · Mathematics 2021-02-02 Robert Beinert , Marzieh Hasannasab

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

We consider signal reconstruction from the norms of subspace components generalizing standard phase retrieval problems. In the deterministic setting, a closed reconstruction formula is derived when the subspaces satisfy certain cubature…

Probability · Mathematics 2017-09-04 Christine Bachoc , Martin Ehler

In this short note we propose a simple two-stage sparse phase retrieval strategy that uses a near-optimal number of measurements, and is both computationally efficient and robust to measurement noise. In addition, the proposed strategy is…

Numerical Analysis · Mathematics 2015-04-27 Mark Iwen , Aditya Viswanathan , Yang Wang

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

In the phase retrieval problem, an unknown vector is to be recovered given quadratic measurements. This problem has received considerable attention in recent times. In this paper, we present an algorithm to solve a nonconvex formulation of…

Information Theory · Computer Science 2016-06-13 Ritesh Kolte , Ayfer Özgür

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

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

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

We consider the problem of recovering signals from their power spectral density. This is a classical problem referred to in literature as the phase retrieval problem, and is of paramount importance in many fields of applied sciences. In…

Information Theory · Computer Science 2013-11-12 Kishore Jaganathan , Samet Oymak , Babak Hassibi

The problem of phase retrieval is a classic one in optics and arises when one is interested in recovering an unknown signal from the magnitude (intensity) of its Fourier transform. While there have existed quite a few approaches to phase…

Information Theory · Computer Science 2015-10-28 Kishore Jaganathan , Yonina C. Eldar , Babak Hassibi

We present the first phase retrieval algorithm guaranteed to solve the multidimensional phase retrieval problem in polynomial arithmetic complexity without prior information. The method successfully terminates in O(N log(N)) operations for…

Image and Video Processing · Electrical Eng. & Systems 2024-07-02 Cole Brabec , Sivan Trajtenberg-Mills , Luca Daniel , Dirk Englund

In this paper we consider the following real-valued and finite dimensional specific instance of the 1-D classical phase retrieval problem. Let ${\bf F}\in\mathbb{R}^N$ be an $N$-dimensional vector, whose discrete Fourier transform has a…

Numerical Analysis · Mathematics 2016-04-26 Ben Leshem , Oren Raz , Ariel Jaffe , Boaz Nadler

The problem of recovering a vector from the absolute values of its inner products against a family of measurement vectors has been well studied in mathematics and engineering. A generalization of this phase retrieval problem also exists in…

Functional Analysis · Mathematics 2013-07-19 Jameson Cahill , Peter G. Casazza , Jesse Peterson , Lindsey Woodland

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

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 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

We investigate the recovery of vectors from magnitudes of frame coefficients when the frames have a low redundancy, meaning a small number of frame vectors compared to the dimension of the Hilbert space. We first show that for vectors in d…

Functional Analysis · Mathematics 2013-02-25 Bernhard G. Bodmann , Nathaniel Hammen