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Related papers: Absolute Uniqueness of Phase Retrieval with Random…

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Consider a scenario in which an unknown signal is transformed by a known linear operator, and then the pointwise absolute value of the unknown output function is reported. This scenario appears in several applications, and the goal is to…

Information Theory · Computer Science 2014-03-10 Dustin G. Mixon

The retrieval of phases from intensity measurements is a key process in many fields in science, from optical microscopy to x-ray crystallography. Here we study phase retrieval of a one-dimensional multi-phase object that is illuminated by…

Quantum Physics · Physics 2016-02-16 Liat Liberman , Yonatan Israel , Eilon Poem , Yaron Silberberg

Phase singularities are locations where light is twisted like a corkscrew, with positive or negative topological charge depending on the twisting direction. Among the multitude of singularities arising in random wave fields, some can be…

Optics · Physics 2018-07-04 L. De Angelis , F. Alpeggiani , A. Di Falco , L. Kuipers

Recent advances in implicit neural representations and differentiable rendering make it possible to simultaneously recover the geometry and materials of an object from multi-view RGB images captured under unknown static illumination.…

Computer Vision and Pattern Recognition · Computer Science 2022-04-15 Yuanqing Zhang , Jiaming Sun , Xingyi He , Huan Fu , Rongfei Jia , Xiaowei Zhou

Recovering a signal from its Fourier magnitude is referred to as phase retrieval, which occurs in different fields of engineering and applied physics. This paper gives a new characterization of the phase retrieval problem. Particularly…

Information Theory · Computer Science 2020-07-16 Wing Hong Wong , Yifei Lou , Stefano Marchesini , Tieyong Zeng

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

We study phase retrieval from magnitude measurements of an unknown signal as an algebraic estimation problem. Indeed, phase retrieval from rank-one and more general linear measurements can be treated in an algebraic way. It is verified that…

Functional Analysis · Mathematics 2014-02-18 Franz J Király , Martin Ehler

The problem of recovering a signal from its Fourier magnitude is of paramount importance in various fields of engineering and applied physics. Due to the absence of Fourier phase information, some form of additional information is required…

Information Theory · Computer Science 2016-05-25 Kishore Jaganathan , Yonina C. Eldar , Babak Hassibi

We consider the robust phase retrieval problem of recovering the unknown signal from the magnitude-only measurements, where the measurements can be contaminated by both sparse arbitrary corruption and bounded random noise. We propose a new…

Machine Learning · Statistics 2018-01-08 Jinghui Chen , Lingxiao Wang , Xiao Zhang , Quanquan Gu

We demonstrate experimentally and theoretically that a coherent image of a pure phase object may be obtained by use of a spatially incoherent illumination beam. This is accomplished by employing a two-beam source of entangled photons…

Phase retrieval problem has been studied in various applications. It is an inverse problem without the standard uniqueness guarantee. To make complete theoretical analyses and devise efficient algorithms to recover the signal is…

Information Theory · Computer Science 2019-05-22 Ziyang Yuan , Hongxia Wang

Iterative projection algorithms are successfully being used as a substitute of lenses to recombine, numerically rather than optically, light scattered by illuminated objects. Images obtained computationally allow aberration-free…

Optics · Physics 2007-05-23 S. Marchesini

This paper develops uniqueness theory for 3D phase retrieval with finite, discrete measurement data for strong phase objects and weak phase objects, including: (i) {\em Unique determination of (phase) projections from diffraction patterns}…

Information Theory · Computer Science 2023-12-05 Albert Fannjiang

Edidin [3] proved a fundamental result in phase retrieval: Theorem: A family of orthogonal projections $\{P_i\}_{i=1}^m$ does phase retrieval in $\mathbb{R}^n$ if and only if for every $0\not= x\in \mathbb{R}^n$, the family…

Functional Analysis · Mathematics 2021-03-11 Peter G. Casazza , Janet C. Tremain

Fraunhofer diffraction is a well-known phenomenon achieved with most wavelength even without lens. A single-shot intensity measurement of diffraction is generally considered inadequate to reconstruct the original light field, because the…

Image and Video Processing · Electrical Eng. & Systems 2019-12-04 An-Dong Xiong , Xiao-Peng Jin , Wen-Kai Yu , Qing Zhao

The concept of illumination bodies studied in convex geometry is used to amend the halfspace depth for multivariate data. The proposed notion of illumination enables finer resolution of the sample points, naturally breaks ties in the…

Statistics Theory · Mathematics 2021-05-28 Stanislav Nagy , Jiří Dvořák

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

We consider the imaging problem of the reconstruction of a three-dimensional object via optical diffraction tomography under the assumptions of the Born approximation. Our focus lies in the situation that a rigid object performs an…

Numerical Analysis · Mathematics 2024-07-11 Robert Beinert , Michael Quellmalz

In this paper, as opposed to the random phase masks, the structured illuminations with a pixel-dependent deterministic phase shift are considered to derandomize the model setup. The RAAR algorithm is modified to adapt to two or more…

Numerical Analysis · Mathematics 2017-02-01 Ji Li , Tie Zhou

Phase retrieval consists in the recovery of a complex-valued signal from intensity-only measurements. As it pervades a broad variety of applications, many researchers have striven to develop phase-retrieval algorithms. Classical approaches…