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

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... rating 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.