Inverse diffusion theory of photoacoustics

Bal, Guillaume; Uhlmann, Günther

doi:10.1088/0266-5611/26/8/085010

Cited by 151 publications

(312 citation statements)

References 27 publications

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“…Bal et al 44,104 have devised a method for solving the optical inversion which requires neither a linearization nor the iterative updating of the fluence. It is a direct rearrangement of the DA assuming that two (or more) PA images,…”

Section: Direct "Zero-divergence" Methodsmentioning

confidence: 99%

“…5.1), although this can clearly lead to bias if the scattering is not known accurately; by using knowledge of the scattering (and chromophores') wavelength dependence; 42,43 or by using multiple measurements made with different surface illumination patterns. 44,45 A less severe form of ill-posedness is caused by the diffusive nature of the optical propagation, which tends to smear out sharp features in the fluence. This means that high spatial frequencies in the distributions of the optical properties have limited influence on the fluence distribution.…”

Section: Uniqueness and Ill-posednessmentioning

confidence: 99%

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Quantitative spectroscopic photoacoustic imaging: a review

et al. 2012

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Abstract. Obtaining absolute chromophore concentrations from photoacoustic images obtained at multiple wavelengths is a nontrivial aspect of photoacoustic imaging but is essential for accurate functional and molecular imaging. This topic, known as quantitative photoacoustic imaging, is reviewed here. The inverse problems involved are described, their nature (nonlinear and ill-posed) is discussed, proposed solution techniques and their limitations are explained, and the remaining unsolved challenges are introduced.

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Section: Direct "Zero-divergence" Methodsmentioning

confidence: 99%

Section: Uniqueness and Ill-posednessmentioning

confidence: 99%

Quantitative spectroscopic photoacoustic imaging: a review

et al. 2012

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“…We recall that u is modeled as the solution to (4). The incoming condition is imposed experimentally.…”

Section: Inverse Scattering Problems With Internal Datamentioning

confidence: 99%

“…Several results of uniqueness in the reconstruction of the absorption and scattering coefficients have been obtain recently. We refer the reader to e.g., [4,6,7,21], for works on quantitative photoacoustics in the mathematics and bioengineering literatures.…”

Section: Introductionmentioning

confidence: 99%

Quantitative thermo-acoustics and related problems

et al. 2011

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Abstract. Thermo-acoustic tomography is a hybrid medical imaging modality that aims to combine the good optical contrast observed in tissues with the good resolution properties of ultrasounds. Thermo-acoustic imaging may be decomposed into two steps. The first step aims at reconstructing an amount of electromagnetic radiation absorbed by tissues from boundary measurements of ultrasounds generated by the heating caused by these radiations. We assume this first step done. Quantitative thermo-acoustics then consists of reconstructing the conductivity coefficient in the equation modeling radiation from the now known absorbed radiation. This second step is the problem of interested in this paper.Mathematically, quantitative thermo-acoustics consists of reconstructing the conductivity in Maxwell's equations from available internal data that are linear in the conductivity and quadratic in the electric field. We consider several inverse problems of this type with applications in thermo-acoustics as well as in acousto-optics. In this framework, we obtain uniqueness and stability results under a smallness constraint on the conductivity. This smallness constraint is removed in the specific of a scalar model for electromagnetic wave propagation for appropriate illuminations constructed by the method of complex geometric optics (CGO) solutions.

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“…See [13,176] for a review of some of these inverse methods. CGO solutions have been used in these hybrid methods in [15][16][17][18]42,110]. Inverse transport see [14] for applications of 60 solutions to inverse problem for the transport equation.…”

Section: Other Applicationsmentioning

confidence: 99%

Inverse problems: seeing the unseen

2014

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This survey article deals mainly with two inverse problems and the relation between them. The first inverse problem we consider is whether one can determine the electrical conductivity of a medium by making voltage and current measurements at the boundary. This is called electrical impedance tomography and also Calderón's problem since the famous analyst proposed it in the mathematical literature (Calderón in On an inverse boundary value problem. Seminar on numerical analysis and its applications to continuum physics (Rio de Janeiro, 1980), Soc Brasil Mat. Rio de Janeiro, pp. [65][66][67][68][69][70][71][72][73] 1980). The second is on travel time tomography. The question is whether one can determine the anisotropic index of refraction of a medium by measuring the travel times of waves going through the medium. This can be recast as a geometry problem, the boundary rigidity problem. Can we determine a Riemannian metric of a compact Riemannian manifold with boundary by measuring the distance function between boundary points? These two inverse problems concern visibility, that is whether we can determine the internal properties of a medium by making measurements at the boundary. The last topic of this paper considers the opposite issue: invisibility: Can one make objects invisible to different types of waves, including light?Communicated by Ari Laptev.

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Inverse diffusion theory of photoacoustics

Cited by 151 publications

References 27 publications

Quantitative spectroscopic photoacoustic imaging: a review

Quantitative spectroscopic photoacoustic imaging: a review

Quantitative thermo-acoustics and related problems

Inverse problems: seeing the unseen

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