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Related papers: Thermoacoustic Tomography in Elastic Media

200 papers

This paper deals with the approximation and homogenization of thermoelastic wave model. First, we study the homogenization problem of a weakly coupled thermoelastic wave model with rapidly varying coefficients, using a semigroup approach,…

Analysis of PDEs · Mathematics 2023-06-29 Salem Nafiri

In this paper, we focus on the numerical analysis of quantitative photoacoustic tomography. Our goal is to reconstruct the optical coefficients, i.e., the diffusion and absorption coefficients, using multiple internal observational data.…

Numerical Analysis · Mathematics 2025-05-09 Giovanni S. Alberti , Siyu Cen , Zhi Zhou

The goal of \emph{photoacoustic tomography} (PAT) is to estimate an \emph{initial pressure function} $\varphi$ from pressure data measured at a boundary surrounding the object of interest. This paper is concerned with a time reversal method…

Analysis of PDEs · Mathematics 2014-02-19 Richard Kowar

An initial-boundary value problem for \[ \left\{ \begin{array}{ll} u_{tt} = \big(\gamma(\Theta) u_{xt}\big)_x + au_{xx} - \big(f(\Theta)\big)_x, \qquad & x\in\Omega, \ t>0, \\[1mm] \Theta_t = \Theta_{xx} + \gamma(\Theta) u_{xt}^2 -…

Analysis of PDEs · Mathematics 2025-04-30 Michael Winkler

Photoacoustic tomography (PAT) is a hybrid medical imaging technique that offer high contrast and a high spatial resolution. One challenging mathematical problem associated with PAT is reconstructing the initial pressure of the wave…

Numerical Analysis · Mathematics 2024-07-16 Gyeongha Hwang , Gihyeon Jeon , Sunghwan Moon , Dabin Park

This paper presents a new algorithm, termed \emph{truncated amplitude flow} (TAF), to recover an unknown vector $\bm{x}$ from a system of quadratic equations of the form $y_i=|\langle\bm{a}_i,\bm{x}\rangle|^2$, where $\bm{a}_i$'s are given…

Machine Learning · Statistics 2017-08-22 Gang Wang , Georgios B. Giannakis , Yonina C. Eldar

The problem of recovering coefficients in a diffusion equation is one of the basic inverse problems. Perhaps the most important term is the one that couples the length and time scales and is often referred to as {\it the\/} diffusion…

Analysis of PDEs · Mathematics 2021-01-19 Barbara Kaltenbacher , William Rundell

We introduce a time-dimensional reduction method for the inverse source problem in linear elasticity, where the goal is to reconstruct the initial displacement and velocity fields from partial boundary measurements of elastic wave…

Numerical Analysis · Mathematics 2025-06-17 Trong D. Dang , Chanh V. Le , Khoa D. Luu , Loc H Nguyen

This study focuses on the Rijke tube problem, which includes features relevant to the modeling of thermoacoustic coupling in reactive flows: a compact acoustic source, an empirical model for the heat source, and nonlinearities. This…

Computational Physics · Physics 2015-08-21 Taraneh Sayadi , Vincent Le Chenadec , Peter Schmid , Franck Richecoeur , Marc Massot

Electrical Impedance Tomography (EIT) is a powerful imaging technique with diverse applications, e.g., medical diagnosis, industrial monitoring, and environmental studies. The EIT inverse problem is about inferring the internal conductivity…

Machine Learning · Computer Science 2023-10-31 Derick Nganyu Tanyu , Jianfeng Ning , Andreas Hauptmann , Bangti Jin , Peter Maass

In this article, we study several reconstruction methods for the inverse source problem of photoacoustic tomography (PAT) with spatially variable sound speed and damping. The backbone of these methods is the adjoint operators, which we…

Analysis of PDEs · Mathematics 2018-08-21 Linh V. Nguyen , Markus Haltmeier

A photoionized gas in thermal equilibrium can display a thermal instability, with 3 or more solutions in the multi-branch region of the S-shape curve giving the temperature versus the radiation-to-gas-pressure ratio. Many studies have been…

Astrophysics · Physics 2009-11-11 A. C. Goncalves , S. Collin , A. -M. Dumont , L. Chevallier

In an open bounded real interval $\Omega$, the model for one-dimensional thermoelasticity given by \[ u_{tt} = u_{xx} - \big(f(\Theta)\big)_x, \qquad \Theta_t = \Theta_{xx} - f(\Theta) u_{xt}, \] is considered along with homogeneous…

Analysis of PDEs · Mathematics 2026-02-06 Michael Winkler

Ultrasound Elastography aims to determine the mechanical properties of the tissue by monitoring tissue deformation due to internal or external forces. Tissue deformations are estimated from ultrasound radio frequency (RF) signals and are…

Image and Video Processing · Electrical Eng. & Systems 2021-10-19 Abdelrahman Zayed , Hassan Rivaz

We are concerned with a coupled-physics spectral problem arising in the coupled propagation of acoustic and elastic waves, which is referred to as the acoustic-elastic transmission eigenvalue problem. There are two major contributions in…

Analysis of PDEs · Mathematics 2023-05-04 Huaian Diao , Hongjie Li , Hongyu Liu , Jiexin Tang

We consider the Cauchy problem for the wave equation in $\Omega\times{\mathbb R}$ with data given on some part of the boundary $\partial\Omega\times{\mathbb R}$. We provide a reconstruction algorithm for this problem based on analytic…

Analysis of PDEs · Mathematics 2018-10-31 M. N. Demchenko

We analyze the mathematical model of multiwave tomography with a variable speed with integrating measurements on planes tangent to a sphere surrounding the source. We prove sharp uniqueness and stability estimates with full and partial data…

Analysis of PDEs · Mathematics 2016-05-04 Plamen Stefanov , Yang Yang

A periodically-uneven (in one horizontal direction) stress-free boundary covering a linear, isotropic, homogeneous, lossless solid half space is submitted to a vertically-propagating shear-horizontal plane, body wave. The rigorous theory of…

Computational Physics · Physics 2018-05-28 Armand Wirgin

An acoustic wave equation for pressure accounting for viscoelastic attenuation is derived from viscoelastic equations of motion. It is assumed that the relaxation moduli are completely monotonic. The acoustic equation differs significantly…

Mathematical Physics · Physics 2014-01-31 Andrzej Hanyga

This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency…

Numerical Analysis · Mathematics 2016-10-06 Giovanni S. Alberti , Habib Ammari , Bangti Jin , Jin-Keun Seo , Wenlong Zhang