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We consider the mathematical model of photoacoustic and thermoacoustic tomography in media with a variable sound speed. When the sound speed is known, the explicit reconstruction formula by P. Stefanov and G. Uhlmann (Inverse Problems,…

Analysis of PDEs · Mathematics 2013-07-08 Lauri Oksanen , Gunther Uhlmann

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

Quantitative image reconstruction in photoacoustic tomography requires the solution of a coupled physics inverse problem involvier light transport and acoustic wave propagation. In this paper we address this issue employing the radiative…

Analysis of PDEs · Mathematics 2017-02-16 Markus Haltmeier , Lukas Neumann , Linh V. Nguyen , Simon Rabanser

In this paper, we study the photoacoustic tomography problem for which we seek to recover both the initial state of the pressure field and the wave speed of the medium from the knowledge of a single boundary measurement. The goal is to…

Analysis of PDEs · Mathematics 2020-07-01 Sebastian Acosta

This paper concerns thermoacoustic tomography and photoacoustic tomography, two couple-physics imaging modalities that attempt to combine the high resolution of ultrasound and the high contrast capabilities of electromagnetic waves. We give…

Analysis of PDEs · Mathematics 2015-09-30 Hongyu Liu , Gunther Uhlmann

In thermoacoustic and photoacoustic tomography an electromagnetic wave is sent through a medium, heating it and therefore generating an elastic expansion that in turns generates an acoustic wave that is measured outside the medium. The…

Analysis of PDEs · Mathematics 2023-02-08 Yavar Kian , Gunther Uhlmann

The paper surveys recent progress in establishing uniqueness and developing inversion formulas and algorithms for the thermoacoustic tomography. In mathematical terms, one deals with a rather special inverse problem for the wave equation.…

Analysis of PDEs · Mathematics 2009-02-02 M. Agranovsky , P. Kuchment , L. Kunyansky

We present a new algorithm for reconstructing an unknown source in Thermoacoustic and Photoacoustic Tomography based on the recent advances in understanding the theoretical nature of the problem. We work with variable sound speeds that…

Numerical Analysis · Mathematics 2015-03-17 Jianliang Qian , Plamen Stefanov , Gunther Uhlmann , Hongkai Zhao

We consider a mathematical model of thermoacoustic tomography and other multi-wave imaging techniques with variable sound speed and attenuation. We find that a Neumann series reconstruction algorithm, previously studied under the assumption…

Analysis of PDEs · Mathematics 2012-12-21 Andrew Homan

This paper is concerned with the stability issue in determining absorption and diffusion coefficients in photoacoustic imaging. Assuming that the medium is layered and the acoustic wave speed is known we derive global H\"{o}lder stability…

Analysis of PDEs · Mathematics 2017-07-25 Kui Ren , Faouzi Triki

We consider the problem of thermoacoustic tomography (TAT), in which one needs to reconstruct the initial value of a solution of the wave equation from its value on an observation surface. We show that if some geometric rays for the…

Analysis of PDEs · Mathematics 2009-12-15 Linh V. Nguyen

This paper is concerned with the stability issue in determining absorption and diffusion coefficients in quantitative photoacoustic imaging. Assuming that the optical wave is generated by point sources in a region where the optical…

Analysis of PDEs · Mathematics 2022-03-24 Eric Bonnetier , Mourad Choulli , Faouzi Triki

In this paper, we investigate an inverse random source problem concerned with recovering the strength of a random, uncorrelated acoustic source from correlation measurements of emitted time-harmonic acoustic waves. Such problems arise in…

Numerical Analysis · Mathematics 2026-02-25 Philipp Mickan , Thorsten Hohage

We investigate the problem of recovering the initial displacement f for a solution u of a linear, isotropic, non-homogeneous elastic wave equation, given measurements of u on [0,T] x \partial \Omega, where \Omega\subset\R^3 is some bounded…

Analysis of PDEs · Mathematics 2015-05-28 Justin Tittelfitz

We study the fixed angle inverse scattering problem of determining a sound speed from scattering measurements corresponding to a single incident wave. The main result shows that a sound speed close to constant can be stably determined by…

Analysis of PDEs · Mathematics 2023-04-25 Shiqi Ma , Leyter Potenciano-Machado , Mikko Salo

An inverse problem of the determination of an initial condition in a hyperbolic equation from the lateral Cauchy data is considered. This problem has applications to the thermoacoustic tomography, as well as to linearized coefficient…

Mathematical Physics · Physics 2007-12-04 Michael V Klibanov , Sergey I Kabanikhin , Dmitriy V Nechaev , Andrey V Kuzhuget

We recover the higher order terms for the acoustic wave equation from measurements of the modulus of the solution. The recovery of these coefficients is reduced to a question of stability for inverting a Hamiltonian flow transform, not the…

Analysis of PDEs · Mathematics 2016-07-14 Joonas Ilmavirta , Alden Waters

This paper investigates photoacoustic tomography with two spatially varying acoustic parameters, the compressibility and the density. We consider the reconstruction of the absorption density parameter (imaging parameter of Photoacoustics)…

Optimization and Control · Mathematics 2016-01-05 Zakaria Belhachmi , Thomas Glatz , Otmar Scherzer

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

Photoacoustic tomography is an emerging medical imaging technology whose primary aim is to map the high-contrast optical properties of biological tissues by leveraging high-resolution ultrasound measurements. Mathematically, this can be…

Analysis of PDEs · Mathematics 2025-02-14 Alessandro Felisi
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