A continuous adjoint for photo-acoustic tomography of the brain. (5th June 2018)

• Record Type: Journal Article
• Authors: Javaherian, Ashkan; Holman, Sean
• Is Part Of: Inverse problems. Volume 34:Number 8(2018:Aug.)
• Publication Date: 2018-06-05
• Subjects: photo-acoustic tomography -- brain -- continuous adjoint -- absorption and dispersion -- frequency power law -- fractional Laplacian; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aac530
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: 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.