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We deal with the photoacoustic imaging modality using dielectric nanoparticles as contrast agents. Exciting the heterogeneous tissue, localized in a bounded domain $\Omega$, with an electromagnetic wave, at a given incident frequency,…

Analysis of PDEs · Mathematics 2020-03-09 Ahcene Ghandriche , Mourad Sini

Increasing the imaging speed is a central aim in photoacoustic tomography. This issue is especially important in the case of sequential scanning approaches as applied for most existing optical detection schemes. In this work we address this…

Numerical Analysis · Mathematics 2016-11-23 Markus Haltmeier , Thomas Berer , Sunghwan Moon , Peter Burgholzer

Standard photoacoustic tomography (PAT) provides data that consist of time-dependent signals governed by the wave equation, which are measured on an observation surface. In contrast, the measured data from the recently invented full-field…

Numerical Analysis · Mathematics 2024-06-10 Ngoc Do , Markus Haltmeier , Richard Kowar , Linh V. Nguyen , Robert Nuster

Photoacoustic tomography (PAT) is a rapidly-evolving medical imaging modality that combines optical absorption contrast with ultrasound imaging depth. One challenge in PAT is image reconstruction with inadequate acoustic signals due to…

We study an inverse problem for a coupled system of semilinear Helmholtz equations where we are interested in reconstructing multiple coefficients in the system from internal data measured in applications such as thermoacoustic imaging. We…

Analysis of PDEs · Mathematics 2023-07-06 Kui Ren , Nathan Soedjak

We consider the inverse source problem of thermo- and photoacoustic tomography, with data registered on an open surface partially surrounding the source of acoustic waves. Under the assumption of constant speed of sound we develop an…

Analysis of PDEs · Mathematics 2020-04-17 Mtthias Eller , Philip Hoskins , Leonid Kunyansky

The development of efficient and accurate image reconstruction algorithms is one of the cornerstones of computed tomography. Existing algorithms for quantitative photoacoustic tomography currently operate in a two-stage procedure: First an…

Analysis of PDEs · Mathematics 2015-05-20 Markus Haltmeier , Lukas Neumann , Simon Rabanser

We derive an explicit method for reconstructing singularities of the initial data in a thermoacoustic tomography problem, in the case of variable sound speed and limited boundary data. In order to obtain this explicit formula we assume the…

Analysis of PDEs · Mathematics 2009-05-19 Dustin Steinhauer

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

Photo-acoustic tomography (PAT) aims to leverage the photo-acoustic coupling between optical absorption of light sources and ultrasound (US) emission to obtain high contrast reconstructions of optical parameters with the high resolution of…

Analysis of PDEs · Mathematics 2016-09-21 Guillaume Bal , Amir Moradifam

The objective of quantitative photoacoustic tomography (QPAT) is to reconstruct optical and thermodynamic properties of heterogeneous media from data of absorbed energy distribution inside the media. There have been extensive theoretical…

Medical Physics · Physics 2019-10-08 Alexander V. Mamonov , Kui Ren

Most reconstruction algorithms for photoacoustic imaging assume that the pressure field is measured by ultrasound sensors placed on a detection surface. However, such sensors do not measure pressure exactly due to their non-uniform…

Analysis of PDEs · Mathematics 2021-01-05 Sebastian Acosta

While in standard photoacoustic imaging the propagation of sound waves is modeled by the standard wave equation, our approach is based on a generalized wave equation with variable sound speed and material density, respectively. In this…

Analysis of PDEs · Mathematics 2018-04-18 Alexander Beigl , Peter Elbau , Kamran Sadiq , Otmar Scherzer

Ultrasound attenuation is caused by absorption and scattering in tissue and is thus a function of tissue composition, hence its imaging offers great potential for screening and differential diagnosis. In this paper we propose a novel method…

Signal Processing · Electrical Eng. & Systems 2019-10-15 Richard Rau , Ozan Unal , Dieter Schweizer , Valery Vishnevskiy , Orcun Goksel

In this tutorial, we combine the different scientific fields of information theory, thermodynamics, regularization theory and non-destructive imaging, especially for photoacoustic and photothermal imaging. The goal is to get a better…

Applied Physics · Physics 2020-12-02 Peter Burgholzer , Guenther Mayr , Gregor Thummerer , Markus Haltmeier

This article addresses the inverse problem of simultaneously recovering both the wave speed coefficient and an unknown initial condition (acting as the source) for the multidimensional wave equation from a single passive boundary…

Analysis of PDEs · Mathematics 2025-07-29 Yavar Kian , Hongyu Liu

Thermo- and photo- acoustic tomography require reconstructing initial acoustic pressure in a body from time series of pressure measured on a surface surrounding the body. For the classical case of free space wave propagation, various…

Analysis of PDEs · Mathematics 2015-06-23 B. Holman , L. Kunyansky

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

Quantitative photo-acoustic tomography (QPAT) seeks to reconstruct a distribution of optical attenuation coefficients inside a sample from a set of time series of pressure data that is measured outside the sample. The associated inverse…

Optimization and Control · Mathematics 2019-09-04 Ashkan Javaherian , Sean Holman

Objective:Optoacoustic (photoacoustic) tomography is aimed at reconstructing maps of the initial pressure rise induced by the absorption of light pulses in tissue. In practice, due to inaccurate assumptions in the forward model, noise and…

Medical Physics · Physics 2019-01-21 Jaya Prakash , Subhamoy Mandal , Daniel Razansky , Vasilis Ntziachristos