Mathematical models and reconstruction methods in magneto-acoustic imaging

Ammari, Habib; Capdeboscq, Yves; Kang, Hyeonbae; Kozhemyak, Anastasia

doi:10.1017/s0956792509007888

Cited by 56 publications

(57 citation statements)

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“…For the mathematical aspects of the first step in thermo-and photo-acoustics, namely the reconstruction of the absorbed radiation map from boundary acoustic wave measurements, we refer the reader to e.g. [1,9,10,12,13,14,17,19,22]. Serious difficulties may need to be addressed in this first step, such as e.g.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 99%

“…Serious difficulties may need to be addressed in this first step, such as e.g. limited data, spatially varying acoustic sound speed [1,14,22], and the effects of acoustic wave attenuation [16]. In this paper, we assume that the absorbed radiation map has been reconstructed satisfactorily.…”

Section: Introductionmentioning

confidence: 99%

Quantitative thermo-acoustics and related problems

et al. 2011

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“…Since [24], internal energies have been used to provide efficient imaging procedures, see [3,6,5,14,21,28].…”

Section: Expansion Formulasmentioning

confidence: 99%

“…Multi-wave systems are capable of high-resolution and high-contrast imaging [1]. A few particular examples of emerging modalities are of great current interest in the biomedical imaging community and will be investigated in detail: magnetic resonance electrical impedance tomography (MREIT) [24,29], [28], magnetic resonance elastography (MRE) [7], impedance-acoustic tomography [21], photo-acoustic [33,25,4] and acousto-optic imaging [14], magneto-acoustic imaging [6], and vibro-acoustography [19].…”

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confidence: 99%

Microwave Imaging by Elastic Deformation

Ammari¹,

Capdeboscq²,

Gournay³

et al. 2011

SIAM J. Appl. Math.

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“…photonic crystals), see [3][4][5]. The main feature of these problems is that they are defined by differential operators which have jumping coefficients.…”

Section: Introductionmentioning

confidence: 99%

Error control for $$hp$$ -adaptive approximations of semi-definite eigenvalue problems

2012

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The nal publication is available at Springer via http://dx.doi.org/10.1007/s00607-012-0260-6. Additional information:Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. ERROR CONTROL FOR hp-ADAPTIVE APPROXIMATIONS OF SEMI-DEFINITE EIGENVALUE PROBLEMSSTEFANO GIANI, LUKA GRUBIŠIĆ, AND JEFFREY S. OVALLAbstract. We present reliable a-posteriori error estimates for hp-adaptive finite element approximations of semi-definite eigenvalue/eigenvector problems. Our model problems are motivated by the applications in photonic crystal eigenvalue computations. We present detailed numerical experiments confirming our theory and give several benchmark results which could serve the purpose of numerical testing of other adaptive procedures.

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Mathematical models and reconstruction methods in magneto-acoustic imaging

Cited by 56 publications

References 14 publications

Quantitative thermo-acoustics and related problems

Quantitative thermo-acoustics and related problems

Microwave Imaging by Elastic Deformation

Error control for $$hp$$ -adaptive approximations of semi-definite eigenvalue problems

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