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We describe a new approach for incorporating prior knowledge into any machine learning algorithm. We aim at applications in physics and signal processing in which we know that certain operations must beembedded into the algorithm. Any operation that allows computation of a gradient or sub-gradient towards its inputs is suited for our mathematical framework. We proof that the inclusion of such prior knowledge reduces maximal error bounds and reduces the number of free parameters. We apply this approach to various tasks ranging from CT image reconstruction over vessel segmentation to the derivation of previously unknown imaging algorithms. As such the concept is widely applicable for many researchers in physics, imaging, and signal processing. We assume that our analysis will support further investigation of this idea in many other fields of physics, imaging, and signal processing.
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