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The problem of recovering a pair of signals from their blind phaseless short-time Fourier transform measurements arises in several important phase retrieval applications, including ptychography and ultra-short pulse characterization. In…

Information Theory · Computer Science 2019-04-11 Tamir Bendory , Dan Edidin , Yonina C. Eldar

A new method recovers the phase difference of interfering wavefronts from a pattern of interference fringes, avoiding the phase discontinuity problem. The method relies on the numerical solution of one-dimensional first-order ordinary…

Optics · Physics 2024-08-01 V. Berejnov , B. Y. Rubinstein

We consider the phase retrieval problem, in which the observer wishes to recover a $n$-dimensional real or complex signal $\mathbf{X}^\star$ from the (possibly noisy) observation of $|\mathbf{\Phi} \mathbf{X}^\star|$, in which…

Information Theory · Computer Science 2022-10-03 Antoine Maillard , Florent Krzakala , Yue M. Lu , Lenka Zdeborová

Inverse problem to recover simultaneously a scalar coefficient, order of a time-fractional derivative, parameters of multiterm fractional Laplacian and a time-dependent source term occurring in a superdiffusion equation from measurements…

Analysis of PDEs · Mathematics 2025-05-06 Hany Gerges , Jaan Janno

This paper addresses the challenging and interesting inverse problem of reconstructing the spatially varying dielectric constant of a medium from phaseless backscattering measurements generated by single-point illumination. The underlying…

Numerical Analysis · Mathematics 2025-06-30 Thuy T. Le , Phuong M. Nguyen , Loc H. Nguyen

In the present paper we study inverse problems related to determining the time-dependent coefficient and unknown source function of fractional heat equations. Our approach shows that having just one set of data at an observation point…

Analysis of PDEs · Mathematics 2024-05-24 Azizbek Mamanazarov , Durvudkhan Suragan

Source extension is a reformulation of inverse problems in wave propagation, that at least in some cases leads to computationally tractable iterative solution methods. The core subproblem in all source extension methods is the solution of a…

Numerical Analysis · Mathematics 2022-04-01 William W. Symes

In the present work, we discuss a unique solvability of an inverse-source problem with integral transmitting condition for time-fractional mixed type equation in a rectangular domain, where the unknown source term depends on space variable…

Analysis of PDEs · Mathematics 2016-04-01 Erkinjon Karimov , Nasser Al-Salti , Sebti Kerbal

We consider the problem of reconstructing the shape of an impenetrable sound-soft obstacle from scattering measurements. The input data is assumed to be the far-field pattern generated when a plane wave impinges on an unknown obstacle from…

Numerical Analysis · Mathematics 2015-05-28 Carlos Borges , Leslie Greengard

Phase retrieval problems occur in a wide range of applications in physics and engineering. Usually, these problems consist in the recovery of an unknown signal from the magnitudes of its Fourier transform. In some applications, however, the…

Numerical Analysis · Mathematics 2021-03-19 Robert Beinert

The Phase Retrieval problem is dealt with for the challenging case where just a single set of (phaseless) radiated field data is available. In particular, even still emulating the solution of crosswords puzzles, we provide decisive…

Signal Processing · Electrical Eng. & Systems 2023-08-16 Giada Maria Battaglia , Andrea Francesco Morabito , Roberta Palmeri , Tommaso Isernia

We focus on an alignment-free method to estimate the underlying signal from a large number of noisy randomly shifted observations. Specifically, we estimate the mean, power spectrum, and bispectrum of the signal from the observations. Since…

Signal Processing · Electrical Eng. & Systems 2018-07-04 Hua Chen , Mona Zehni , Zhizhen Zhao

This article addresses the inverse problem of simultaneously recovering both the wave speed coefficient and an unknown initial condition (acting as the source) for the multidimensional wave equation from a single passive boundary…

Analysis of PDEs · Mathematics 2025-07-29 Yavar Kian , Hongyu Liu

This paper addresses the direct and inverse source problems for the stochastic acoustic, biharmonic, electromagnetic, and elastic wave equations in a unified framework. The driven source is assumed to be a centered generalized microlocally…

Analysis of PDEs · Mathematics 2021-12-28 Jianliang Li , Peijun Li , Xu Wang

This paper investigates an inverse source problem for general semilinear stochastic hyperbolic equations. Motivated by the challenges arising from both randomness and nonlinearity, we develop a globally convergent iterative regularization…

Analysis of PDEs · Mathematics 2025-04-25 Qi Lü , Yu Wang

The spatial dependent unknown acoustic source is reconstructed according noisy multiple frequency data on a remote closed surface. Assume that the unknown function is supported on a bounded domain. To determine the support, we present a…

Numerical Analysis · Mathematics 2019-07-30 Zhiliang Deng , Xiaomei Yang

Considering the ambiguousness of the discrete-time phase retrieval problem to recover a signal from its Fourier intensities, one can ask the question: what additional information about the unknown signal do we need to select the correct…

Numerical Analysis · Mathematics 2020-02-19 Robert Beinert , Gerlind Plonka

An extension may be proposed to the intensity interferometer of Hanbury Brown and Twiss to provide the Fourier phase measurement by the use of third-order intensity correlations. It is well known that interferometric reconstruction of…

Astrophysics · Physics 2008-06-14 B. E. Zhilyaev

The use of simultaneous sources in geophysical inverse problems has revolutionized the ability to deal with large scale data sets that are obtained from multiple source experiments. However, the technique breaks when the data has…

Computational Engineering, Finance, and Science · Computer Science 2014-04-22 Eldad Haber , Mathias Chung

This paper is concerned with the inverse problem to recover the scalar, complex-valued refractive index of a medium from measurements of scattered time-harmonic electromagnetic waves at a fixed frequency. The main results are two…

Numerical Analysis · Mathematics 2017-02-09 Frederic Weidling , Thorsten Hohage