  Circular cone-beam (CCB) Computed Tomography (CT) has become an integral part
of industrial quality control, materials science and medical imaging. The need
to acquire and process each scan in a short time naturally leads to trade-offs
between speed and reconstruction quality, creating a need for fast
reconstruction algorithms capable of creating accurate reconstructions from
limited data.
  In this paper we introduce the Neural Network Feldkamp-Davis-Kress (NN-FDK)
algorithm. This algorithm adds a machine learning component to the FDK
algorithm to improve its reconstruction accuracy while maintaining its
computational efficiency. Moreover, the NN-FDK algorithm is designed such that
it has low training data requirements and is fast to train. This ensures that
the proposed algorithm can be used to improve image quality in high throughput
CT scanning settings, where FDK is currently used to keep pace with the
acquisition speed using readily available computational resources.
  We compare the NN-FDK algorithm to two standard CT reconstruction algorithms
and to two popular deep neural networks trained to remove reconstruction
artifacts from the 2D slices of an FDK reconstruction. We show that the NN-FDK
reconstruction algorithm is substantially faster in computing a reconstruction
than all the tested alternative methods except for the standard FDK algorithm
and we show it can compute accurate CCB CT reconstructions in cases of high
noise, a low number of projection angles or large cone angles. Moreover, we
show that the training time of an NN-FDK network is orders of magnitude lower
than the considered deep neural networks, with only a slight reduction in
reconstruction accuracy.
