  Inspired by the recent advances on minimizing nonsmooth or bound-constrained
convex functions on models using varying degrees of fidelity, we propose a line
search multigrid (MG) method for full-wave iterative image reconstruction in
photoacoustic tomography (PAT) in heterogeneous media. To compute the search
direction at each iteration, we decide between the gradient at the target
level, or alternatively an approximate error correction at a coarser level,
relying on some predefined criteria. To incorporate absorption and dispersion,
we derive the analytical adjoint directly from the first-order acoustic wave
system. The effectiveness of the proposed method is tested on a total-variation
penalized Iterative Shrinkage Thresholding algorithm (ISTA) and its accelerated
variant (FISTA), which have been used in many studies of image reconstruction
in PAT. The results show the great potential of the proposed method in
improving speed of iterative image reconstruction.
