Photoacoustic imaging is a comparably young medical imaging method combining diffuse optical tomography and ultrasonography allowing for images with optical contrast and acoustical resolution. An object of interest is irradiated with a short time laser pulse and the laser light distributes within the object according to its optical properties. Optical absorption converts a part of the energy to heat accompanied by thermal expansion which induces pressure waves in the ultrasound range. Inverse analysis of the ultrasound signal allows for conclusions on the optical and mechanical properties of the underlying material.
At our institute, we are developing a reconstruction algorithm solving a reaction-diffusion system for the light transport with standard FEM and the acoustical wave equation by use of the hybridizable discontinuous Galerkin method. The calculation of the gradient of the objective function is based on the solution of the adjoint equations. In this way, we are able to solve the inverse problem efficiently while taking account of the relevant physical phenomena.