Deep learning for photoacoustic tomography from sparse data. Issue 7 (3rd July 2019)

• Record Type: Journal Article
• Authors: Antholzer, Stephan; Haltmeier, Markus; Schwab, Johannes
• Is Part Of: Inverse problems in science and engineering. Volume 27:Issue 7(2019)
• Page Start: 987
• Page End: 1005
• Publication Date: 2019-07-03
• Subjects: Photoacoustic tomography -- sparse data -- image reconstruction -- deep learning -- convolutional neural networks -- inverse problems; 92C55 -- 45Q05 -- 65R32; Engineering mathematics -- Periodicals; Inverse problems (Differential equations) -- Periodicals; 620.001515357
• DOI: 10.1080/17415977.2018.1518444
• Languages: English
• ISSNs: 1741-5977

Abstract

ABSTRACT: 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 CNN, which does not require time-consuming solution of 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 state of the art iterative approaches for PAT from sparse data.