  Biomedical photoacoustic tomography, which can provide high resolution 3D
soft tissue images based on the optical absorption, has advanced to the stage
at which translation from the laboratory to clinical settings is becoming
possible. The need for rapid image formation and the practical restrictions on
data acquisition that arise from the constraints of a clinical workflow are
presenting new image reconstruction challenges. There are many classical
approaches to image reconstruction, but ameliorating the effects of incomplete
or imperfect data through the incorporation of accurate priors is challenging
and leads to slow algorithms. Recently, the application of Deep Learning, or
deep neural networks, to this problem has received a great deal of attention.
This paper reviews the literature on learned image reconstruction, summarising
the current trends, and explains how these new approaches fit within, and to
some extent have arisen from, a framework that encompasses classical
reconstruction methods. In particular, it shows how these new techniques can be
understood from a Bayesian perspective, providing useful insights. The paper
also provides a concise tutorial demonstration of three prototypical approaches
to learned image reconstruction. The code and data sets for these
demonstrations are available to researchers. It is anticipated that it is in in
vivo applications - where data may be sparse, fast imaging critical and priors
difficult to construct by hand - that Deep Learning will have the most impact.
With this in mind, the paper concludes with some indications of possible future
research directions.
