  We discuss several methods for image reconstruction in compressed sensing
photoacoustic tomography (CS-PAT). In particular, we apply the deep learning
method of [H. Li, J. Schwab, S. Antholzer, and M. Haltmeier. NETT: Solving
Inverse Problems with Deep Neural Networks (2018), arXiv:1803.00092], which is
based on a learned regularizer, for the first time to the CS-PAT problem. We
propose a network architecture and training strategy for the NETT that we
expect to be useful for other inverse problems as well. All algorithms are
compared and evaluated on simulated data, and validated using experimental data
for two different types of phantoms. The results on the one the hand indicate
great potential of deep learning methods, and on the other hand show that
significant future work is required to improve their performance on real-word
data.
