English
Related papers

Related papers: Phase retrieval for sub-Gaussian measurements

200 papers

Phase retrieval, a long-established challenge for recovering a complex-valued signal from its Fourier intensity measurements, has attracted significant interest because of its far-flung applications in optical imaging. To enhance accuracy,…

Signal Processing · Electrical Eng. & Systems 2023-05-16 Qiuliang Ye , Bingo Wing-Kuen Ling , Li-Wen Wang , Daniel Pak-Kong Lun

Phase retrieval refers to recovering a signal from its Fourier magnitude. This problem arises naturally in many scientific applications, such as ultra-short laser pulse characterization and diffraction imaging. Unfortunately, phase…

Information Theory · Computer Science 2018-04-05 Tamir Bendory , Dan Edidin , Yonina C. Eldar

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

We address the phase retrieval problem with errors in the sensing vectors. A number of recent methods for phase retrieval are based on least squares (LS) formulations which assume errors in the quadratic measurements. We extend this…

Signal Processing · Electrical Eng. & Systems 2022-02-02 Sidharth Gupta , Ivan Dokmanić

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 work introduces a novel Fourier phase retrieval model, called polarimetric phase retrieval that enables a systematic use of polarization information in Fourier phase retrieval problems. We provide a complete characterization of…

Signal Processing · Electrical Eng. & Systems 2022-06-28 Julien Flamant , Konstantin Usevich , Marianne Clausel , David Brie

Gabor phase retrieval stands for recovering a square integrable function up to a global phase from absolute values of its Gabor transform. In this paper, we study Gabor phase retrieval from discrete samples. We consider three types of…

Classical Analysis and ODEs · Mathematics 2025-12-02 Ting Chen , Hanwen Lu , Wenchang Sun

Reconstructing a signal from squared linear (rank-one quadratic) measurements is a challenging problem with important applications in optics and imaging, where it is known as phase retrieval. This paper proposes two new phase retrieval…

Information Theory · Computer Science 2016-09-21 Cheng Qian , Nicholas D. Sidiropoulos , Kejun Huang , Lei Huang , H. C. So

Phase retrieval (PR) is a crucial problem in many imaging applications. This study focuses on resolving the holographic phase retrieval problem in situations where the measurements are affected by a combination of Poisson and Gaussian…

Signal Processing · Electrical Eng. & Systems 2023-09-22 Zongyu Li , Jason Hu , Xiaojian Xu , Liyue Shen , Jeffrey A. Fessler

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 retrieval is an important problem with significant physical and industrial applications. In this paper, we consider the case where the magnitude of the measurement of an underlying signal is corrupted by Gaussian noise. We introduce a…

Optimization and Control · Mathematics 2022-05-03 Jianwei Niu , Hok Shing Wong , Tieyong Zeng

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 propose a general framework for reconstructing transform-sparse images from undersampled (squared)-magnitude data corrupted with outliers. This framework is implemented using a multi-layered approach, combining multiple initializations…

In this paper we tackle the problem of recovering the phase of complex linear measurements when only magnitude information is available and we control the input. We are motivated by the recent development of dedicated optics-based hardware…

Machine Learning · Computer Science 2020-02-17 Sidharth Gupta , Rémi Gribonval , Laurent Daudet , Ivan Dokmanić

We consider a least absolute deviation (LAD) approach to the robust phase retrieval problem that aims to recover a signal from its absolute measurements corrupted with sparse noise. To solve the resulting non-convex optimization problem, we…

Signal Processing · Electrical Eng. & Systems 2024-04-25 Seonho Kim , Kiryung Lee

Phase retrieval with prior information can be cast as a nonsmooth and nonconvex optimization problem. We solve the problem by graph projection splitting (GPS), where the two proximity subproblems and the graph projection step can be solved…

Optimization and Control · Mathematics 2020-06-24 Ji Li , Hongkai Zhao

Interferometric inversion involves recovery of a signal from cross-correlations of its linear transformations. A close relative of interferometric inversion is the generalized phase retrieval problem, which consists of recovering a signal…

Signal Processing · Electrical Eng. & Systems 2020-11-10 Bariscan Yonel , Birsen Yazici

Reconstruction of multidimensional signals from the samples of their partial derivatives is known to be a standard problem in inverse theory. Such and similar problems routinely arise in numerous areas of applied sciences, including optical…

Numerical Analysis · Computer Science 2015-05-30 Mohammad Rostami , Oleg Michailovich , Zhou Wang

Suppose we wish to recover a signal x in C^n from m intensity measurements of the form |<x,z_i>|^2, i = 1, 2,..., m; that is, from data in which phase information is missing. We prove that if the vectors z_i are sampled independently and…

Information Theory · Computer Science 2011-09-22 Emmanuel J. Candes , Thomas Strohmer , Vladislav Voroninski

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