  The idea of replacing hardware by software to compensate for scattered
radiation in flat-panel X-ray imaging is well established in the literature.
Recently, deep-learningbased image translation approaches, most notably the
U-Net, have emerged for scatter estimation. These yield considerable
improvements over model-based methods. Such networks, however, involve
potential drawbacks that need to be considered. First, they are trained in a
data-driven fashion without making use of prior knowledge and X-ray physics.
Second, due to their high parameter complexity, the validity of deep neural
networks is difficult to assess. To circumvent these issues, we introduce here
a surrogate function to model X-ray scatter distributions that can be expressed
by few parameters. We could show empirically that cubic B-splines are
well-suited to model X-ray scatter in the diagnostic energy regime. Based on
these findings, we propose a lean convolutional encoder architecture that
extracts local scatter characteristics from X-ray projection images. These
characteristics are embedded into a global context using a constrained
weighting matrix yielding spline coefficients that model the scatter
distribution. In a first simulation study with 17 thorax data sets, we could
show that our method and the U-Net-based state of the art reach about the same
accuracy. However, we could achieve these comparable outcomes with orders of
magnitude fewer parameters while ensuring that not high-frequency information
gets manipulated.
