
An inverse source problem for the stochastic wave equation
This paper is concerned with an inverse source problem for the stochasti...
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On the simultaneous recovery of the conductivity and the nonlinear reaction term in a parabolic equation
This paper considers the inverse problem of recovering both the unknown,...
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On the identification of the nonlinearity parameter in the Westervelt equation from boundary measurements
We consider an undetermined coefficient inverse problem for a non linea...
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On a three dimensional Compton scattering tomography system with fixed source
Compton scatter tomography is an emerging technique with attractive appl...
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Reconstruction, with tunable sparsity levels, of shearwave velocity profiles from surface wave data
The analysis of surface wave dispersion curves is a way to infer the ver...
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Numerical analysis of a wave equation for lossy media obeying a frequency power law
We study a wave equation with a nonlocal time fractional damping term th...
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Quantitative PAT with simplified P_N approximation
The photoacoustic tomography (PAT) is a hybrid modality that combines th...
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Fractional time stepping and adjoint based gradient computation in an inverse problem for a fractionally damped wave equation
In this paper we consider the inverse problem of identifying the initial data in a fractionally damped wave equation from time trace measurements on a surface, as relevant in photoacoustic or thermoacoustic tomography. We derive and analyze a time stepping method for the numerical solution of the corresponding forward problem. Moreover, to efficiently obtain reconstructions by minimizing a Tikhonov regularization functional (or alternatively, by computing the MAP estimator in a Bayesian approach), we develop an adjoint based scheme for gradient computation. Numerical reconstructions in two space dimensions illustrate the performance of the devised methods.
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