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Related papers: Phase retrieval from low-rate samples

200 papers

Phase retrieval in dynamical sampling is a novel research direction, where an unknown signal has to be recovered from the phaseless measurements with respect to a dynamical frame, i.e. a sequence of sampling vectors constructed by the…

Numerical Analysis · Mathematics 2021-03-19 Robert Beinert , Marzieh Hasannasab

This paper discusses the noisy phase retrieval problem: recovering a complex image signal with independent noise from quadratic measurements. Inspired by the dark fringes shown in the measured images of the array detector, a novel phase…

Computer Vision and Pattern Recognition · Computer Science 2022-04-14 Wen-Kai Yu , An-Dong Xiong , Xu-Ri Yao , Guang-Jie Zhai , Qing Zhao

Phase retrieval refers to a classical nonconvex problem of recovering a signal from its Fourier magnitude measurements. Inspired by the compressed sensing technique, signal sparsity is exploited in recent studies of phase retrieval to…

Computational Physics · Physics 2013-02-04 Zai Yang , Cishen Zhang , Lihua Xie

We propose a flexible convex relaxation for the phase retrieval problem that operates in the natural domain of the signal. Therefore, we avoid the prohibitive computational cost associated with "lifting" and semidefinite programming (SDP)…

Information Theory · Computer Science 2017-03-17 Sohail Bahmani , Justin Romberg

While characterization of coherent wavefields is essential to laser, x-ray and electron imaging, sensors measure the squared magnitude of the field, rather than the field itself. Holography or phase retrieval must be used to characterize…

Image and Video Processing · Electrical Eng. & Systems 2020-12-10 David J. Brady , Timothy J. Schulz , Chengyu Wang

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 2018-06-22 Ali Ahmed , Alireza Aghasi , Paul Hand

In this work, we present some new results for compressed sensing and phase retrieval. For compressed sensing, it is shown that if the unknown $n$-dimensional vector can be expressed as a linear combination of $s$ unknown Vandermonde vectors…

Information Theory · Computer Science 2024-02-16 Dzevdan Kapetanovic

Phase retrieval seeks to recover a signal x from the amplitude |Ax| of linear measurements. We cast the phase retrieval problem as a non-convex quadratic program over a complex phase vector and formulate a tractable relaxation (called…

Optimization and Control · Mathematics 2013-07-23 Irène Waldspurger , Alexandre d'Aspremont , Stéphane Mallat

Line spectral estimation theory aims to estimate the off-the-grid spectral components of a time signal with optimal precision. Recent results have shown that it is possible to recover signals having sparse line spectra from few temporal…

Information Theory · Computer Science 2017-01-31 Maxime Ferreira Da Costa , Wei Dai

This paper considers the question of recovering the phase of an object from intensity-only measurements, a problem which naturally appears in X-ray crystallography and related disciplines. We study a physically realistic setup where one can…

Information Theory · Computer Science 2013-11-08 Emmanuel Candes , Xiaodong Li , Mahdi Soltanolkotabi

We describe a new algorithm to solve a particular phase retrieval problem, that has wide applications in audio processing: the reconstruction of a function from its scalogram, that is from the modulus of its wavelet transform. It is a…

Optimization and Control · Mathematics 2017-04-11 Irène Waldspurger

Phase retrieval problems in antenna measurements arise when a reference phase cannot be provided to all measurement locations. Phase retrieval algorithms require sufficiently many independent measurement samples of the radiated fields to be…

Signal Processing · Electrical Eng. & Systems 2022-06-24 Josef Knapp , Alexander Paulus , Jonas Kornprobst , Uwe Siart , Thomas F. Eibert

Phase retrieval is known to always be unstable when using a frame or continuous frame for an infinite dimensional Hilbert space. We consider a generalization of phase retrieval to the setting of subspaces of $L_2$ which coincides with using…

Functional Analysis · Mathematics 2022-03-08 Robert Calderbank , Ingrid Daubechies , Daniel Freeman , Nikki Freeman

We improve a phase retrieval approach that uses correlation-based measurements with compactly supported measurement masks [27]. The improved algorithm admits deterministic measurement constructions together with a robust, fast recovery…

Numerical Analysis · Mathematics 2016-12-07 Mark A. Iwen , Brian Preskitt , Rayan Saab , Aditya Viswanathan

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

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

In diffraction imaging, one is tasked with reconstructing a signal from its power spectrum. To resolve the ambiguity in this inverse problem, one might invoke prior knowledge about the signal, but phase retrieval algorithms in this vein…

Functional Analysis · Mathematics 2013-06-26 Afonso S. Bandeira , Yutong Chen , Dustin G. Mixon

This work examines the multi-view compressive phase retrieval problem in a distributed sensor network, where each sensor device, limited by storage and sensing capabilities, can access only intensity measurements from an unknown part of the…

Information Theory · Computer Science 2025-06-02 Ming-Hsun Yang

In many signal processing problems arising in practical applications, we wish to reconstruct an unknown signal from its phaseless measurements with respect to a frame. This inverse problem is known as the phase retrieval problem. For each…

Information Theory · Computer Science 2023-07-04 Palina Salanevich

This paper considers the recovery of continuous time signals from the magnitude of its samples. It uses a combination of structured modulation and oversampling and provides sufficient conditions on the signal and the sampling system such…

Information Theory · Computer Science 2013-02-19 Fanny Yang , Volker Pohl , Holger Boche