Quantitative thermoacoustic tomography with microwaves sources

Akhouayri, Hassan; Bergounioux, Maı̈tine; Silva, Anabela Da; Elbau, Peter; Litman, Amélie; Mindrinos, Leonidas

doi:10.1515/jiip-2016-0012

Cited by 12 publications

(30 citation statements)

References 35 publications

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“…We investigate the so called quantitative thermoacoustic tomography process (e.g. [1,5,23,25] and their references). According to [5], assuming that the variations in temperature and pressure are weak and neglecting the nonlinear effects, we obtain the system…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Carleman estimates and some inverse problems for the coupled quantitative thermoacoustic equations by boundary data. Part I: Carleman estimates

Shang¹,

Li²

2020

Preprint

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In this paper, we consider Carleman estimates and inverse problems for the coupled quantitative thermoacoustic equations. In Part I, we establish Carleman estimates for the coupled quantitative thermoacoustic equations by assuming that the coefficients satisfy suitable conditions and taking the usual weight function ϕ(x, t) = e λψ(x,t) , ψ(x, t) = |x − x 0 | 2 − β (t − t 0 ) 2 + βt 2 0 for x in a bounded domain in R n with C 3 -boundary and t ∈ (0, T ), where t 0 = T /2. We will discuss applications of the Carleman estimates to some inverse problems for the coupled quantitative thermoacoustic equations in the succeeding Part II paper [6].

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Carleman estimates and some inverse problems for the coupled quantitative thermoacoustic equations by boundary data. Part I: Carleman estimates

Shang¹,

Li²

2020

Preprint

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“…Precisely, we do not use any reconstruction formula (exact of not) to deal with the inverse problem. Following [1,6,7] philosophy, we rather include the unknown parameter in a cost functional in a least-squared sense. So far, both the reconstruction of p 0 and the sensors location question will be addressed in the same functional.…”

Section: Modeling the Problem 21 The Pde (Direct) Model And The Senso...mentioning

confidence: 99%

“…• The first system of equations describes the generation of the heating process inside the body. In the PAT, this system involves the fluence equation (the fluence rate is the average of the light intensity in all directions) which is a diffusion equation [6]; in the TAT case, this equation is replaced by Maxwell equations [1]. Then the temperature is driven by the classical heat equation, than can be neglected in the PAT case because the high speed of light implies that the thermal effect is quasi instantaneous.…”

Section: Introductionmentioning

confidence: 99%

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How to position sensors in thermo-acoustic tomography

2019

Self Cite

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Thermo-acoustic tomography is a non-invasive medical imaging technique, constituting a precise and cheap alternative to X-imaging. The principle is to excite a body to reconstruct with a pulse inducing an inhomogeneous heating and therefore expansion of tissues. This creates an acoustic wave pressure which is measured with sensors. The reconstruction of heterogeneities inside the body can be then performed by solving an inverse problem, knowing measurements of the acoustic waves outside the body. As the intensity of the measured pressure is expected to be small, a challenging problem consists in locating the sensors in a adequate way.This paper is devoted to the determination of an optimal sensors location to achieve this reconstruction. We first introduce a model involving a least square functional standing for an observation of the pressure for a first series of measures by sensors, and an observability-like constant functional describing for the quality of reconstruction. Then, we determine an appropriate location of sensors for two series of measures, in two steps: first, we reconstruct possible initial data by solving a worst-case design like problem. Second, we determine from the knowledge of these initial conditions the optimal location of sensors for observing in the best way the corresponding solution of the wave equation.Far from providing an intrinsic solution to the general issue of locating sensors, solving this problem allows to determine a new sensors location improving the quality of reconstruction before getting a new series of measures.We perform a mathematical analysis of this model: in particular we investigate existence issues and introduce a numerical algorithm to solve it. Eventually, several numerical 2D simulations illustrate our approach.2 Modeling the problem 2.1 The PDE (direct) model and the sensors set Throughout this paper, we will use the notation 1 A to denote the characteristic function of a set A ⊂ IR d (d ≥ 1) which is the function equal to 1 on A and 0 elsewhere.

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“…Note that, in this work, we are not concerned with the so-called "quantitative part" of the photoacoustic technique (see e.g. [1,11,12,17]) but only with the issue of recovering the source term H.…”

Section: Introduction and Motivationsmentioning

confidence: 99%

A time reversal algorithm in acoustic media with Dirac measure approximations

Bretin¹,

Lucas²,

Privat³

2018

Inverse Problems

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This article is devoted to the study of a photoacoustic tomography model, where one is led to consider the solution of the acoustic wave equation with a source term writing as a separated variables function in time and space, whose temporal component is in some sense close to the derivative of the Dirac distribution at t = 0. This models a continuous wave laser illumination performed during a short interval of time. We introduce an algorithm for reconstructing the space component of the source term from the measure of the solution recorded by sensors during a time T all along the boundary of a connected bounded domain. It is based at the same time on the introduction of an auxiliary equivalent Cauchy problem allowing to derive explicit reconstruction formula and then to use of a deconvolution procedure. Numerical simulations illustrate our approach. Finally, this algorithm is also extended to elasticity wave systems.

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Quantitative thermoacoustic tomography with microwaves sources

Cited by 12 publications

References 35 publications

Carleman estimates and some inverse problems for the coupled quantitative thermoacoustic equations by boundary data. Part I: Carleman estimates

Carleman estimates and some inverse problems for the coupled quantitative thermoacoustic equations by boundary data. Part I: Carleman estimates

How to position sensors in thermo-acoustic tomography

A time reversal algorithm in acoustic media with Dirac measure approximations

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