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In this paper, we consider the inverse problem of recovering a sound soft scatterer from the measured scattered field. The scattered field is assumed to be induced by a point source on a curve/surface that is known. Here we will propose and…

Analysis of PDEs · Mathematics 2021-10-22 Isaac Harris

In this work, we are devoted to the reconstruction of an unknown initial value from the terminal data. The asymptotic and root-distribution properties of Mittag-Leffler functions are used to establish stability of the backward problem.…

Numerical Analysis · Mathematics 2025-06-24 Dakang Cen , Zhiyuan Li , Wenlong Zhang

For problems of time-harmonic scattering by polygonal obstacles, embedding formulae provide a useful means of computing the far-field coefficient induced by any incident plane wave, given the far-field coefficient of a relatively small set…

Numerical Analysis · Mathematics 2018-05-24 Andrew Gibbs , Stephen Langdon , Andrea Moiola

In this paper, we consider the inverse shape problem of recovering isotropic scatterers with a conductive boundary condition. Here, we assume that the measured far-field data is known at a fixed wave number. Motivated by recent work, we…

Analysis of PDEs · Mathematics 2023-05-25 Rafael Ceja Ayala , Isaac Harris , Andreas Kleefeld

In this paper, we consider a regularization strategy for the factorization method when there is noise added to the data operator. The factorization method is a qualitative method used in shape reconstruction problems. These methods are…

Analysis of PDEs · Mathematics 2023-04-05 Isaac Harris

Spatial sound field interpolation relies on suitable models to both conform to available measurements and predict the sound field in the domain of interest. A suitable model can be difficult to determine when the spatial domain of interest…

Audio and Speech Processing · Electrical Eng. & Systems 2022-11-30 Manuel Hahmann , Efren Fernandez-Grande

This paper studies the problem of parameter estimation in resonant, acoustic fluid-structure interaction problems over a wide frequency range. Problems with multiple resonances are known to be subjected to local minima, which represents a…

Computational Physics · Physics 2019-03-06 Peter Göransson , Jacques Cuenca , Timo Lähivaara

Generally, wave field reconstructions obtained by phase-retrieval algorithms are noisy, blurred and corrupted by various artifacts such as irregular waves, spots, etc. These disturbances, arising due to many factors such as non-idealities…

Optics · Physics 2012-07-24 Artem Migukin , Mostafa Agour , Vladimir Katkovnik

This article present a new method to reconstruct slowly varying width defects in 2D waveguides using one-side section measurements at locally resonant frequencies. At these frequencies, locally resonant modes propagate in the waveguide up…

Numerical Analysis · Mathematics 2022-12-15 Angèle Niclas , Laurent Seppecher

In this paper we present a convergence analysis for the Nystrom method proposed in [Jour. Comput. Phys. 169 pp. 2921-2934, 2001] for the solution of the combined boundary integral equation formulations of sound-soft acoustic scattering…

Numerical Analysis · Mathematics 2012-10-12 Oscar P. Bruno , Victor Dominguez , Francisco-Javier Sayas

We perform extended studies of an adaptive finite element method applied to the reconstruction of shapes of buried objects from experimental backscattering data. We use experimental data which are collected by a microwave scattering…

Numerical Analysis · Mathematics 2015-03-05 Larisa Beilina , Nguyen Trung Thành , Michael V. Klibanov , John Bondestam Malmberg

A unified method for three-dimensional reconstruction of objects from transmission images collected at multiple illumination directions is described. The method may be applicable to experimental conditions relevant to absorption-based,…

Medical Physics · Physics 2022-12-07 Timur E. Gureyev , Hamish G. Brown , Harry M. Quiney , Leslie J. Allen

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

Newton's method is a fundamental technique in optimization with quadratic convergence within a neighborhood around the optimum. However reaching this neighborhood is often slow and dominates the computational costs. We exploit two…

Machine Learning · Computer Science 2016-05-24 Hadi Daneshmand , Aurelien Lucchi , Thomas Hofmann

In this paper, we propose a new method that combines the inexact Newton method with a procedure to obtain a feasible inexact projection for solving constrained smooth and nonsmooth equations. The local convergence theorems are established…

Optimization and Control · Mathematics 2019-03-19 Fabiana R. de Oliveira , Orizon P. Ferreira

The attempt to solve inverse scattering problems often leads to optimization and sampling problems that require handling moderate to large amounts of partial differential equations acting as constraints. We focus here on determining…

Numerical Analysis · Mathematics 2025-04-09 Carolina Abugattas , Ana Carpio , Elena Cebrián , Gerardo Oleaga

We investigate the inverse source problem for the wave equation, arising in photo- and thermoacoustic tomography. There exist quite a few theoretically exact inversion formulas explicitly expressing solution of this problem in terms of the…

Analysis of PDEs · Mathematics 2018-08-01 Ngoc Do , Leonid Kunyansky

We present a novel Newton-type method for distributed optimization, which is particularly well suited for stochastic optimization and learning problems. For quadratic objectives, the method enjoys a linear rate of convergence which provably…

Machine Learning · Computer Science 2014-05-15 Ohad Shamir , Nathan Srebro , Tong Zhang

We study the shape reconstruction of an inclusion from the {faraway} measurement of the associated electric field. This is an inverse problem of practical importance in biomedical imaging and is known to be notoriously ill-posed. By…

Numerical Analysis · Mathematics 2022-01-25 Ming-Hui Ding , Hongyu Liu , Guang-Hui Zheng

This paper is devoted to studying the global and finite convergence of the semi-smooth Newton method for solving a piecewise linear system that arises in cone-constrained quadratic programming problems and absolute value equations. We first…

Optimization and Control · Mathematics 2023-01-24 Nicolas F. Armijo , Yunier Bello-Cruz , Gabriel Haeser