A Neumann series based method for photoacoustic tomography on irregular domains

Recently, a Neumann series based numerical method is developed for photoacoustic tomography in a paper by Qian, Stefanov, Uhlmann, and Zhao [An efficient neumann series-based algorithm for thermoacoustic and photoacoustic tomography with variable sound speed. SIAM J. Imag. Sci., 4:850–883, 2011]. It is an efficient and convergent numerical scheme that recovers the initial condition of an acoustic wave equation with non-constant sound speeds by boundary measurements. In practical applications, the domains of interest typically have irregular geometries and contain media with discontinuous sound speeds, and these issues pose challenges for the development of efficient solvers. In this paper, we propose a new algorithm which is based on the use of the staggered discontinuous Galerkin method for solving the underlying wave propagation problem. It gives a convenient way to handle domains with complex geometries and discontinuous sound speeds. Our numerical results show that the method is able to recover the initial condition accurately.