Deep Learning for Photoacoustic Tomography from Sparse Data

The development of fast and accurate image reconstruction algorithms is a central aspect of computed tomography. In this paper we investigate this issue for the sparse data problem in photoacoustic tomography (PAT). We develop a direct and highly efficient reconstruction algorithm based on deep learning. In our approach image reconstruction is performed with a deep convolutional neural network (CNN), whose weights are adjusted prior to the actual image reconstruction based on a set of training data. The proposed reconstruction approach can be interpreted as a network that uses the PAT filtered backprojection algorithm for the first layer, followed by the U-net architecture for the remaining layers. Actual image reconstruction with deep learning consists in one evaluation of the trained network. The numerical complexity of evaluating the trained network is smaller than that of iterative reconstruction algorithms, which require repeatedly solving the forward and adjoint problems. At the same time, our numerical results demonstrate that the proposed deep learning approach reconstructs images with a quality comparable to (or even outperforming) state of the art iterative approaches for PAT from sparse data.