A continuous adjoint for photo-acoustic tomography of the brain

作者：Javaherian Ashkan^*; Holman Sean

来源：Inverse Problems, 2018, 34(8): 085003.

DOI：10.1088/1361-6420/aac530

• photo-acoustic tomography
• brain
• continuous adjoint
• absorption and dispersion
• frequency power law
• fractional Laplacian

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.

• 出版日期2018-8