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In photoacoustic tomography, one is interested to recover the initialpressure distribution inside a tissue from the corresponding measurements ofthe induced acoustic wave on the boundary of a region enclosing the tissue. Inthe limited view problem, the wave boundary measurements are given on the partof the boundary, whereas in the full view problem, the measurements are knownon the whole boundary. For the full view problem, there exist various fast androbust reconstruction methods. These methods give severe reconstructionartifacts when they are applied directly to the limited view data. One approachfor reducing such artefacts is trying to extend the limited view data to thewhole region boundary, and then use existing reconstruction methods for thefull view data. In this paper, we propose an operator learning approach forconstructing an operator that gives an approximate extension of the limitedview data. We consider the behavior of a reconstruction formula on the extendedlimited view data that is given by our proposed approach. Approximation errorsof our approach are analyzed. We also present numerical results with theproposed extension approach supporting our theoretical analysis.

Operator learning approach for the limited view problem in photoacoustic tomography