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We propose a new approach for studying the notion of the instantaneous frequency of a signal. We build on ideas from the Synchrosqueezing theory of Daubechies, Lu and Wu and consider a variant of Synchrosqueezing, based on the short-time…

Numerical Analysis · Mathematics 2012-01-17 Gaurav Thakur , Hau-Tieng Wu

Source footprints represent an inherent problem to full-waveform inversion (FWI). They are caused by the high data sensitivity to the model parameters in the vicinity of the seismic sources and can be exacerbated by source-related errors in…

Geophysics · Physics 2025-06-12 Milad Bader , Robert G. Clapp , Kurt T. Nihei , Biondo Biondi

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

We investigate the use of spatial interpolation methods for reconstructing the horizontal near-surface wind field given a sparse set of measurements. In particular, random Fourier features is compared to a set of benchmark methods including…

Numerical Analysis · Mathematics 2022-01-19 Jonas Kiessling , Emanuel Ström , Raúl Tempone

The main goal of this paper is to estimate the regional acoustic and geoacoustic shallow-water environment from data collected by a vertical hydrophone array and transmitted by distant time-harmonic point sources. We aim at estimating the…

Analysis of PDEs · Mathematics 2019-09-04 Laure Dumaz , Josselin Garnier , Guilhem Lepoultier

We propose an inverse scattering scheme of recovering a polyhedral obstacle in $\mathbb{R}^n$, $n=2,3$, by only a few high-frequency acoustic backscattering measurements. The obstacle could be sound-soft or sound-hard. It is shown that the…

Analysis of PDEs · Mathematics 2015-02-05 Jingzhi Li , Hongyu Liu

Reconstructing continuous signals from a small number of discrete samples is a fundamental problem across science and engineering. In practice, we are often interested in signals with 'simple' Fourier structure, such as bandlimited,…

Data Structures and Algorithms · Computer Science 2018-12-24 Haim Avron , Michael Kapralov , Cameron Musco , Christopher Musco , Ameya Velingker , Amir Zandieh

A new algorithm is proposed for solving the three-dimensional scalar inverse problem of acoustic sounding in an inhomogeneous medium. The data for the algorithm are the complex amplitudes of the wave field measured outside the inhomogeneity…

Numerical Analysis · Mathematics 2019-11-26 A. B. Bakushinsky , A. S. Leonov

This paper is devoted to a novel quantitative imaging scheme of identifying impenetrable obstacles in time-harmonic acoustic scattering from the associated far-field data. The proposed method consists of two phases. In the first phase, we…

Numerical Analysis · Mathematics 2023-07-05 Youzi He , Hongyu Liu , Xianchao Wang

Stochastic inverse problems considered in this article consist of estimating the probability distributions of intrinsically random inputs of computer models. These estimations are based on observable outputs affected by model noise, and…

Statistics Theory · Mathematics 2025-03-17 Nicolas Bousquet , Mélanie Blazère , Thomas Cerbelaud

The inverse problem of reconstructing a source term from boundary measurements, for the wave equation, is revisited. We propose a novel approach to recover the unknown source through measuring the wave fields after injecting small…

Analysis of PDEs · Mathematics 2021-12-03 Mourad Sini , Haibing Wang

We study an inverse random obstacle scattering problems in $\mathbb{R}^2$ where the scatterer is formulated by a Gaussian process defined on the angular parameter domain. Equipped with a modified covariance function which is mathematically…

Numerical Analysis · Mathematics 2026-02-02 Zhiqi Sun , Xiang Xu , Yiwen Lin

I discuss approaches to optimally remove noise from images. A generalization of Wiener filtering to Non-Gaussian distributions and wavelets is described, as well as an approach to measure the errors in the reconstructed images. We argue…

Astrophysics · Physics 2009-10-31 Ue-Li Pen

This paper addresses the problem of expressing a signal as a sum of frequency components (sinusoids) wherein each sinusoid may exhibit abrupt changes in its amplitude and/or phase. The Fourier transform of a narrow-band signal, with a…

Machine Learning · Computer Science 2013-02-27 Yin Ding , Ivan W. Selesnick

In this paper, a new model is proposed for the inverse random source scattering problem of the Helmholtz equation with attenuation. The source is assumed to be driven by a fractional Gaussian field whose covariance is represented by a…

Analysis of PDEs · Mathematics 2019-11-27 Peijun Li , Xu Wang

In this paper, we present algorithms for reconstructing an unknown compact scatterer embedded in a random noisy background medium, given measurements of the scattered field and information about the background medium and the sound profile.…

Numerical Analysis · Mathematics 2019-01-29 Carlos Borges , George Biros

Consider the problem of inverse scattering of time-harmonic point sources from an infinite, penetrable rough interface with bounded obstacles buried in the lower half-space, where the interface is assumed to be a local perturbation of a…

Analysis of PDEs · Mathematics 2020-09-02 Jianliang Li , Jiaqing Yang , Bo Zhang

This paper is concerned with a numerical method for a 3D coefficient inverse problem with phaseless scattering data. These are multi-frequency data generated by a single direction of the incident plane wave. Our numerical procedure consists…

Numerical Analysis · Mathematics 2017-10-16 Michael V. Klibanov , Dinh-Liem Nguyen , Loc H. Nguyen

In a series of recent papers (Adcock, Hansen and Poon, 2013, Appl. Comput. Harm. Anal. 45(5):3132-3167), (Adcock, Gataric and Hansen, 2014, SIAM J. Imaging Sci. 7(3):1690-1723) and (Adcock, Hansen, Kutyniok and Ma, 2015, SIAM J. Math. Anal.…

Numerical Analysis · Mathematics 2016-03-08 Milana Gataric , Clarice Poon

This paper studies the recovery of a superposition of point sources from noisy bandlimited data. In the fewest possible words, we only have information about the spectrum of an object in a low-frequency band bounded by a certain cut-off…

Information Theory · Computer Science 2013-07-11 Emmanuel Candes , Carlos Fernandez-Granda