  In this paper, we consider the problem of feature reconstruction from
incomplete x-ray CT data. Such problems occurs, e.g., as a result of dose
reduction in the context medical imaging. Since image reconstruction from
incomplete data is a severely ill-posed problem, the reconstructed images may
suffer from characteristic artefacts or missing features, and significantly
complicate subsequent image processing tasks (e.g., edge detection or
segmentation). In this paper, we introduce a novel framework for the robust
reconstruction of convolutional image features directly from CT data, without
the need of computing a reconstruction firs. Within our framework we use
non-linear (variational) regularization methods that can be adapted to a
variety of feature reconstruction tasks and to several limited data situations
. In our numerical experiments, we consider several instances of edge
reconstructions from angularly undersampled data and show that our approach is
able to reliably reconstruct feature maps in this case.
