Singular Values of the Attenuated Photoacoustic Imaging Operator

Elbau, Peter; Scherzer, Otmar; Shi, Cong

doi:10.48550/arxiv.1611.05807

Cited by 2 publications

(6 citation statements)

References 3 publications

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“…Here h : R d → R is the photoacoustic (PA) source, c 0 > 0 is a constant, and D α is the time convolution operator associated with the inverse Fourier transform of the complex valued attenuation function α : R → C. Dissipative pressure wave equation models that can be cast in the form (1.1) can be found in [16,29,38,39,42,43,51,66,67]. The particular form of α depends on the used acoustic attenuation model and various different models have been proposed for PAT (see [42] for an overview).…”

Section: Introductionmentioning

confidence: 99%

Iterative methods for photoacoustic tomography in attenuating acoustic media

2017

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The development of efficient and accurate reconstruction methods is an important aspect of tomographic imaging. In this article, we address this issue for photoacoustic tomography. To this aim, we use models for acoustic wave propagation accounting for frequency dependent attenuation according to a wide class of attenuation laws that may include memory. We formulate the inverse problem of photoacoustic tomography in attenuating medium as an illposed operator equation in a Hilbert space framework that is tackled by iterative regularization methods. Our approach comes with a clear convergence analysis. For that purpose we derive explicit expressions for the adjoint problem that can efficiently be implemented. In contrast to time reversal, the employed adjoint wave equation is again damping and, thus has a stable solution. This stability property can be clearly seen in our numerical results. Moreover, the presented numerical results clearly demonstrate the efficiency and accuracy of the derived iterative reconstruction algorithms in various situations including the limited view case.

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Section: Introductionmentioning

confidence: 99%

Iterative methods for photoacoustic tomography in attenuating acoustic media

2017

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“…Mathematically this is encoded in the function κ defining the pseudo-differential operator A κ . A physically and mathematically meaningful κ has to satisfy the following properties (see [4]):…”

Section: Attenuationmentioning

confidence: 99%

“…The four conditions in Definition 2.1 on κ encode the following physical properties of the attenuated wave equation (see [4]):…”

Section: Remarkmentioning

confidence: 99%

“…For such attenuation coefficients we proved in [4] well-posedness of the attenuated wave equation: Lemma 2.3 Let κ be an attenuation coefficient. Then the solution p a of the equation (1.2) exists and is a real-valued tempered distribution in R × R 3 .…”

Section: Remarkmentioning

confidence: 99%

“…The literature on Photoacoustics in attenuating media concentrates on time-reversal and attenuation compensation based on power laws: We mention the k-wave toolbox implementation and the according papers [3,24], [2,7]. In [4] several attenuation laws from the literature have been cataloged into two classes, namely weak and strong attenuation laws. Power laws lead, in general, to severely ill-posed photoacoustic imaging problem, while mathematically sophisticatedly derived models, like the Nachman-Smith-Waag model [15], lead to moderately ill-posed problems.…”

Section: Introductionmentioning

confidence: 99%

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Reconstruction formulas for photoacoustic imaging in attenuating media

Scherzer

Shi

2017

Inverse Problems

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In this paper we study the problem of photoacoustic inversion in a weakly attenuating medium. We present explicit reconstruction formulas in such media and show that the inversion based on such formulas is moderately ill-posed. Moreover, we present a numerical algorithm for imaging and demonstrate in numerical experiments the feasibility of this approach. arXiv:1705.07466v1 [math.NA] 21 May 2017 R, appearing as a source term in the wave equationfrom some measurements over time of the pressure p on a two-dimensional manifold Γ outside of the specimen, that is outside of the support of the absorption density function. This problem has been studied extensively in the literature (see e.g. [14,25,13], to mention just a few survey articles). Biological tissue has a non-vanishing viscosity, thus there is thermal consumption of energy. These effects can be described mathematically by attenuation. Common models of such are the thermo-viscous model [9], its modification [11], Szabo's power law [22, 21] and a causal modification [10], Hanyga & Seredy'nska [5], Sushilov & Cobbold [20], and the Nachman-Smith-Waag model [15]. Photoacoustic imaging in attenuating medium then consists in computing the absorption density function h from measurements of the attenuated pressure p a on a surface containing the object of interest. The attenuated pressure equation reads as follows

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Singular Values of the Attenuated Photoacoustic Imaging Operator

Cited by 2 publications

References 3 publications

Iterative methods for photoacoustic tomography in attenuating acoustic media

Iterative methods for photoacoustic tomography in attenuating acoustic media

Reconstruction formulas for photoacoustic imaging in attenuating media

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