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We consider the inverse problem of determining a general semilinear term appearing in nonlinear parabolic equations. For this purpose, we derive a new criterion that allows to prove global recovery of some general class of semilinear terms…

Analysis of PDEs · Mathematics 2020-11-13 Yavar Kian , Gunther Uhlmann

Phase retrieval deals with the recovery of complex- or real-valued signals from magnitude measurements. As shown recently, the method PhaseMax enables phase retrieval via convex optimization and without lifting the problem to a higher…

Information Theory · Computer Science 2018-02-02 Ramina Ghods , Andrew S. Lan , Tom Goldstein , Christoph Studer

Phaseless reconstruction from space-time samples is a nonlinear problem of recovering a function $x$ in a Hilbert space $\mathcal{H}$ from the modulus of linear measurements $\{\lvert \langle x, \phi_i\rangle \rvert$, $ \ldots$, $\lvert…

Functional Analysis · Mathematics 2017-06-19 Akram Aldroubi , llya krishtal , Sui Tang

Polarimetric imaging captures surface polarization characteristics, such as the Degree of Linear Polarization (DoLP) and the Angle of Polarization (AoP). In mainstream Division of-Focal-Plane (DoFP) color polarization imaging, recovering…

Computer Vision and Pattern Recognition · Computer Science 2026-05-12 Chenggong Li , Yidong Luo , Junchao Zhang , Boxin Shi , Degui Yang

The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and…

Data Analysis, Statistics and Probability · Physics 2017-05-01 Wenxu Wang , Ying-Cheng Lai , Celso Grebogi

The state of polarization and the carrier phase drift dynamically during transmission in a random fashion in coherent optical fiber communications. The typical digital signal processing solution to mitigate these impairments consists of two…

Information Theory · Computer Science 2024-01-25 Cristian B. Czegledi , Erik Agrell , Magnus Karlsson , Pontus Johannisson

We study the classical problem of recovering a multidimensional source signal from observations of nonlinear mixtures of this signal. We show that this recovery is possible (up to a permutation and monotone scaling of the source's original…

Machine Learning · Statistics 2023-01-18 Alexander Schell , Harald Oberhauser

In this paper, we propose a new non-convex algorithm for solving the phase retrieval problem, i.e., the reconstruction of a signal $ \vx\in\H^n $ ($\H=\R$ or $\C$) from phaseless samples $ b_j=\abs{\langle \va_j, \vx\rangle } $, $…

Numerical Analysis · Mathematics 2020-10-15 Bing Gao , Xinwei Sun , Yang Wang , Zhiqiang Xu

The problem of recovering a one-dimensional signal from its Fourier transform magnitude, called Fourier phase retrieval, is ill-posed in most cases. We consider the closely-related problem of recovering a signal from its phaseless…

Information Theory · Computer Science 2017-07-25 Tamir Bendory , Yonina C. Eldar , Nicolas Boumal

We consider the inverse problem of recovering a continuous-domain function from a finite number of noisy linear measurements. The unknown signal is modeled as the sum of a slowly varying trend and a periodic or quasi-periodic seasonal…

Functional Analysis · Mathematics 2025-05-16 Julien Fageot

A general mathematical framework and recovery algorithm is presented for the holographic phase retrieval problem. In this problem, which arises in holographic coherent diffraction imaging, a "reference" portion of the signal to be recovered…

Information Theory · Computer Science 2024-12-20 David A. Barmherzig , Ju Sun , T. J. Lane , Po-Nan Li , Emmanuel J. Candès

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 study algorithms for solving quadratic systems of equations based on optimization methods over polytopes. Our work is inspired by a recently proposed convex formulation of the phase retrieval problem, which estimates the unknown signal…

Information Theory · Computer Science 2018-05-25 Oussama Dhifallah , Christos Thrampoulidis , Yue M. Lu

Sampling in shift-invariant spaces is a realistic model for signals with smooth spectrum. In this paper, we consider phaseless sampling and reconstruction of real-valued signals in a shift-invariant space from their magnitude measurements…

Information Theory · Computer Science 2017-02-22 Cheng Cheng , Junzheng Jiang , Qiyu Sun

This work takes the first steps towards solving the "phaseless subspace tracking" (PST) problem. PST involves recovering a time sequence of signals (or images) from phaseless linear projections of each signal under the following structural…

Machine Learning · Computer Science 2018-09-13 Seyedehsara Nayer , Namrata Vaswani

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

In this work we propose a nonconvex two-stage \underline{s}tochastic \underline{a}lternating \underline{m}inimizing (SAM) method for sparse phase retrieval. The proposed algorithm is guaranteed to have an exact recovery from $O(s\log n)$…

Numerical Analysis · Mathematics 2022-11-23 Jian-Feng Cai , Yuling Jiao , Xiliang Lu , Juntao You

Dynamical sampling deals with signals that evolve in time under the action of a linear operator. The purpose of the present paper is to analyze the performance of the basic dynamical sampling algorithms in the finite dimensional case and…

Numerical Analysis · Mathematics 2018-10-16 Akram Aldroubi , Longxiu Huang , Ilya Krishtal , Akos Ledeczi , Roy R. Lederman , Peter Volgyesi

In this manuscript we demonstrate a method to reconstruct the wavefront of focused beams from a measured diffraction pattern behind a diffracting mask in real-time. The phase problem is solved by means of a neural network, which is trained…

Image and Video Processing · Electrical Eng. & Systems 2021-04-07 Jonathon White , Sici Wang , Wilhelm Eschen , Jan Rothhardt

We analyze continuous-time mirror descent applied to sparse phase retrieval, which is the problem of recovering sparse signals from a set of magnitude-only measurements. We apply mirror descent to the unconstrained empirical risk…

Machine Learning · Statistics 2020-10-21 Fan Wu , Patrick Rebeschini