Operator learning approach for the limited view problem in photoacoustic tomography
For researchers in photoacoustic tomography, this offers a data-driven approach to mitigate artifacts from limited-view measurements, though it is incremental as it builds on existing extension-and-reconstruct strategies.
The paper tackles the limited view problem in photoacoustic tomography, where measurements are only available on part of the boundary. They propose an operator learning method to extend limited view data to the full boundary, enabling the use of full-view reconstruction methods, and provide theoretical error analysis and numerical validation.
In photoacoustic tomography, one is interested to recover the initial pressure distribution inside a tissue from the corresponding measurements of the induced acoustic wave on the boundary of a region enclosing the tissue. In the limited view problem, the wave boundary measurements are given on the part of the boundary, whereas in the full view problem, the measurements are known on the whole boundary. For the full view problem, there exist various fast and robust reconstruction methods. These methods give severe reconstruction artifacts when they are applied directly to the limited view data. One approach for reducing such artefacts is trying to extend the limited view data to the whole region boundary, and then use existing reconstruction methods for the full view data. In this paper, we propose an operator learning approach for constructing an operator that gives an approximate extension of the limited view data. We consider the behavior of a reconstruction formula on the extended limited view data that is given by our proposed approach. Approximation errors of our approach are analyzed. We also present numerical results with the proposed extension approach supporting our theoretical analysis.