Singular values of the attenuated photoacoustic imaging operator

DOI10.1016/j.jde.2017.06.018zbMath1401.35329arXiv1611.05807OpenAlexW2964330170MaRDI QIDQ1785923

Cong Shi, Otmar Scherzer, Peter Elbau

Publication date: 2 October 2018

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.05807

zbMATH Keywords

inverse problemscompact operatorsingular valuesdegree of ill-posednessattenuated photoacoustic imaging

Mathematics Subject Classification ID

Ill-posed problems for PDEs (35R25) Linear operators and ill-posed problems, regularization (47A52)

Related Items (6)

Fractional time stepping and adjoint based gradient computation in an inverse problem for a fractionally damped wave equation ⋮ Iterative methods for photoacoustic tomography in attenuating acoustic media ⋮ Reconstruction formulas for photoacoustic imaging in attenuating media ⋮ Reconstruction algorithms for photoacoustic tomography in heterogeneous damping media ⋮ Some inverse problems for wave equations with fractional derivative attenuation ⋮ Quantitative inverse problem in visco-acoustic media under attenuation model uncertainty

Cites Work

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• Remarks on the general Funk transform and thermoacoustic tomography
• An introduction to Sobolev spaces and interpolation spaces
• On eigenvalues of differentiable positive definite kernels
• Range descriptions for the spherical mean Radon transform
• Attenuation Models in Photoacoustics
• Introduction to Smooth Manifolds
• Causality analysis of frequency-dependent wave attenuation
• Mathematics of thermoacoustic tomography

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