  We propose a model-based image reconstruction method for photoacoustic
tomography(PAT) involving a novel form of regularization and demonstrate its
ability to recover good quality images from significantly reduced size
datasets. The regularization is constructed to suit the physical structure of
typical PAT images. We construct it by combining second-order derivatives and
intensity into a non-convex form to exploit a structural property of PAT images
that we observe: in PAT images, high intensities and high second-order
derivatives are jointly sparse. The specific form of regularization constructed
here is a modification of the form proposed for fluorescence image restoration.
This regularization is combined with a data fidelity cost, and the required
image is obtained as the minimizer of this cost. As this regularization is
non-convex, the efficiency of the minimization method is crucial in obtaining
artifact-free reconstructions. We develop a custom minimization method for
efficiently handling this non-convex minimization problem. Further, as
non-convex minimization requires a large number of iterations and the PAT
forward model in the data-fidelity term has to be applied in the iterations, we
propose a computational structure for efficient implementation of the forward
model with reduced memory requirements. We evaluate the proposed method on both
simulated and real measured data sets and compare them with a recent
reconstruction method that is based on a well-known fast iterative shrinkage
threshold algorithm (FISTA).
