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The idea of replacing hardware by software to compensate for scatteredradiation in flat-panel X-ray imaging is well established in the literature.Recently, deep-learningbased image translation approaches, most notably theU-Net, have emerged for scatter estimation. These yield considerableimprovements over model-based methods. Such networks, however, involvepotential drawbacks that need to be considered. First, they are trained in adata-driven fashion without making use of prior knowledge and X-ray physics.Second, due to their high parameter complexity, the validity of deep neuralnetworks is difficult to assess. To circumvent these issues, we introduce herea surrogate function to model X-ray scatter distributions that can be expressedby few parameters. We could show empirically that cubic B-splines arewell-suited to model X-ray scatter in the diagnostic energy regime. Based onthese findings, we propose a lean convolutional encoder architecture thatextracts local scatter characteristics from X-ray projection images. Thesecharacteristics are embedded into a global context using a constrainedweighting matrix yielding spline coefficients that model the scatterdistribution. In a first simulation study with 17 thorax data sets, we couldshow that our method and the U-Net-based state of the art reach about the sameaccuracy. However, we could achieve these comparable outcomes with orders ofmagnitude fewer parameters while ensuring that not high-frequency informationgets manipulated.

Deep Scatter Splines: Learning-Based Medical X-ray Scatter Estimation Using B-splines