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

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.