Photoacoustic Tomography and boundary control problems
The acoustic step of Photoacoustic Tomography is an inverse initial source problem for the wave equation. A dual version of this inverse problem is a boundary control problem. This control problem arises as a step in the Boundary Control method that can be used to solve an inverse boundary value problem for the wave equation, that is, the problem to reconstruct a spatially varying sound speed from boundary measurements. We discuss the stability properties of the inverse initial source problem and the boundary control problem, and describe also a stability result for a variant of the Boundary Control method.