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Many man-made objects are characterised by a shape that is symmetric along one or more planar directions. Estimating the location and orientation of such symmetry planes can aid many tasks such as estimating the overall orientation of an…

Computer Vision and Pattern Recognition · Computer Science 2021-07-01 Mihaela Cătălina Stoian , Tommaso Cavallari

An important theme in modern inverse problems is the reconstruction of time-dependent data from only finitely many measurements. To obtain satisfactory reconstruction results in this setting it is essential to strongly exploit temporal…

Numerical Analysis · Mathematics 2024-03-14 Martin Holler , Alexander Schlüter , Benedikt Wirth

The standard approach for photoacoustic imaging with variable speed of sound is time reversal, which consists in solving a well-posed final-boundary value problem for the wave equation backwards in time. This paper investigates the…

Optimization and Control · Mathematics 2016-03-17 Zakaria Belhachmi , Thomas Glatz , Otmar Scherzer

In deep tissue photoacoustic imaging the spatial resolution is inherently limited by the acoustic wavelength. Recently, it was demonstrated that it is possible to surpass the acoustic diffraction limit by analyzing fluctuations in a set of…

A method for photoacoustic tomography is presented that uses circular integrals of the acoustic wave for the reconstruction of a three-dimensional image. Image reconstruction is a two-step process: In the first step data from a stack of…

Numerical Analysis · Mathematics 2009-12-06 G. Zangerl , O. Scherzer , M. Haltmeier

In this article, we revisit iterative methods for solving the inverse problem of photoacoustic tomography in free space. Recently, there have been interesting developments on explicit formulations of the adjoint operator, demonstrating that…

Analysis of PDEs · Mathematics 2017-05-16 Markus Haltmeier , Linh V. Nguyen

We present a comparative study of two qualitative imaging methods in an acoustic waveguide with sound hard walls. The waveguide terminates at one end and contains unknown obstacles of compact support, to be determined from data gathered by…

Analysis of PDEs · Mathematics 2020-01-08 Liliana Borcea , Shixu Meng

We consider travel time tomography problems involving detection of high contrast, discrete high velocity structures. This results in a discrete nonlinear inverse problem, for which traditional grid-based models and iterative linearized…

Data Analysis, Statistics and Probability · Physics 2017-07-07 Yenting Lin , Antonio Ortega

The aim of this paper is to propose for the first time a reconstruction scheme and a stability result for recovering from acoustic-optic data absorption distributions with bounded variation. The paper extends earlier results on smooth…

Analysis of PDEs · Mathematics 2014-05-13 Habib Ammari , Loc Hoang Nguyen , Laurent Seppecher

In ultrasound tomography, the speed of sound inside an object is estimated based on acoustic measurements carried out by sensors surrounding the object. An accurate forward model is a prominent factor for high-quality image reconstruction,…

Image and Video Processing · Electrical Eng. & Systems 2021-11-24 Janne Koponen , Timo Lähivaara , Jari Kaipio , Marko Vauhkonen

This article aims to present a new method to reconstruct slowly varying width defects in 2D waveguides using locally resonant frequencies. At these frequencies, locally resonant modes propagate in the waveguide under the form of Airy…

Mathematical Physics · Physics 2023-04-13 Angèle Niclas , Laurent Seppecher

We consider the problem of reconstructing signals and images from periodic nonlinearities. For such problems, we design a measurement scheme that supports efficient reconstruction; moreover, our method can be adapted to extend to…

Machine Learning · Statistics 2017-10-03 Viraj Shah , Mohammadreza Soltani , Chinmay Hegde

This paper investigates the shape reconstructions of sub-wavelength objects from near-field measurements in transverse electromagnetic scattering. This geometric inverse problem is notoriously ill-posed and challenging. We develop a novel…

Mathematical Physics · Physics 2023-05-03 M. H. Ding , H. Y. Liu , G. H. Zheng

In recent years, metamaterials have gained considerable attention as a promising material technology due to their unique properties and customizable design, distinguishing them from traditional materials. This article delves into the value…

Applied Physics · Physics 2024-04-09 Sichao Qu , Min Yang , Yunfei Xu , Songwen Xiao , Nicholas X. Fang

This paper deals with the resolution of inverse problems in a periodic setting or, in other terms, the reconstruction of periodic continuous-domain signals from their noisy measurements. We focus on two reconstruction paradigms: variational…

Optimization and Control · Mathematics 2018-11-14 Anaïs Badoual , Julien Fageot , Michael Unser

The time reversal symmetry of the wave equation allows wave refocusing back at the source. However, this symmetry does not hold in lossy media. We present a new strategy to compensate wave amplitude losses due to attenuation. The strategy…

Classical Physics · Physics 2022-12-15 Crystal T. Wu , Nuno M. Nobre , Emmanuel Fort , Graham D. Riley , Fumie Costen

Beamforming in ultrasound imaging has significant impact on the quality of the final image, controlling its resolution and contrast. Despite its low spatial resolution and contrast, delay-and-sum is still extensively used nowadays in…

Computer Vision and Pattern Recognition · Computer Science 2016-05-20 Teodora Szasz , Adrian Basarab , Denis Kouamé

Time reversal methods are widely used to achieve wave focusing in acoustics and electromagnetics. A typical time reversal experiment requires that a transmitter be initially present at the target focusing point, which limits the application…

Chaotic Dynamics · Physics 2016-05-11 Bo Xiao , Thomas M. Antonsen , Edward Ott , Steven M. Anlage

We consider an inverse problem for the elastic wave of simultaneously reconstructing the impedance and the geometric information of the bounded body that is occupied by a homogeneous and isotropic elastic medium from the measured Cauchy…

Numerical Analysis · Mathematics 2025-06-26 Yao Sun , Yan Chang , Yukun Guo

We introduce a generalization of time-domain wavefield reconstruction inversion to anisotropic acoustic modeling. Wavefield reconstruction inversion has been extensively researched in recent years for its ability to mitigate cycle skipping.…

Geophysics · Physics 2020-04-17 Mathias Louboutin , Gabrio Rizzuti , Felix J. Herrmann