A continuous adjoint for photo-acoustic tomography of the brain

Ashkan Javaherian, Sean Holman

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    We present an optimisation framework for photo-acoustic tomography of the brain based on a system of coupled equations that describe the propagation of sound waves in linear isotropic inhomogeneous and lossy elastic media with absorption and physical dispersion following a frequency power law using fractional Laplacian operators. The adjoint of the associated continuous forward operator is derived, and a numerical framework for computing this adjoint based on a k-space pseudo-spectral method is presented. We analytically show that the derived continuous adjoint matches the adjoint of an associated discretised forward operator. We include this adjoint in a first-order positivity constrained optimisation algorithm that is regularised by total variation minimisation, and show that the iterates monotonically converge to a minimiser of an objective function, even in the presence of some error in estimating the physical parameters of the medium.
    Original languageEnglish
    JournalInverse Problems
    Early online date16 May 2018
    Publication statusPublished - 5 Jun 2018


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