Mathematics of thermoacoustic tomography

Kuchment, Peter; Kunyansky, Leonid

doi:10.1017/s0956792508007353

Cited by 305 publications

(316 citation statements)

References 117 publications

(296 reference statements)

Supporting

Mentioning

316

Contrasting

Order By: Relevance

“…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%

Quantitative thermo-acoustics and related problems

et al. 2011

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

Quantitative thermo-acoustics and related problems

et al. 2011

View full text Add to dashboard Cite

show abstract

“…In oceanography and meteorology this problem is called data assimilation, see for example Auroux and Blum [3,4], Le Dimet et al [24], Teng et al [34] or Zou et al [40]. Such a problem also arises in the context of medical imaging by impedance-acoustic tomography; see for instance Gebauer and Scherzer [14] and the review paper by Kuchment and Kunyansky [22]. The estimation of the initial state can also be regarded as the main step in solving inverse source problems, see Alvez et al [1].…”

Section: Introductionmentioning

confidence: 99%

Recovering the initial state of an infinite-dimensional system using observers

2010

View full text Add to dashboard Cite

. Recovering the initial state of an infinitedimensional system using observers. Automatica, Elsevier, 2010, 46 (10) Abstract: Let A be the generator of a strongly continuous semigroup T on the Hilbert space X, and let C be a linear operator from D(A) to another Hilbert space Y (possibly unbounded with respect to X, not necessarily admissible). We consider the problem of estimating the initial state z 0 ∈ D(A) (with respect to the norm of X) from the output function y(t) = CT t z 0 , given for all t in a bounded interval [0, τ ]. We introduce the concepts of estimatability and backward estimatability for (A, C) (in a more general way than currently available in the literature), we introduce forward and backward observers, and we provide an iterative algorithm for estimating z 0 from y. This algorithm generalizes various algorithms proposed recently for specific classes of systems and it is an attractive alternative to methods based on inverting the Gramian. Our results lead also to a very general formulation of Russell's principle, i.e., estimatability and backward estimatability imply exact observability. This general formulation of the principle does not require T to be invertible. We illustrate our estimation algorithms on systems described by wave and Schrödinger equations, and we provide results from numerical simulations.

show abstract

“…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].…”

mentioning

confidence: 99%