  Radon transform is widely used in physical and life sciences and one of its
major applications is the X-ray computed tomography (X-ray CT), which is
significant in modern health examination. The Radon inversion or image
reconstruction is challenging due to the potentially defective radon
projections. Conventionally, the reconstruction process contains several ad hoc
stages to approximate the corresponding Radon inversion. Each of the stages is
highly dependent on the results of the previous stage. In this paper, we
propose a novel unified framework for Radon inversion via deep learning (DL).
The Radon inversion can be approximated by the proposed framework with an
end-to-end fashion instead of processing step-by-step with multiple stages. For
simplicity, the proposed framework is short as iRadonMap (inverse Radon
transform approximation). Specifically, we implement the iRadonMap as an
appropriative neural network, of which the architecture can be divided into two
segments. In the first segment, a learnable fully-connected filtering layer is
used to filter the radon projections along the view-angle direction, which is
followed by a learnable sinusoidal back-projection layer to transfer the
filtered radon projections into an image. The second segment is a common neural
network architecture to further improve the reconstruction performance in the
image domain. The iRadonMap is overall optimized by training a large number of
generic images from ImageNet database. To evaluate the performance of the
iRadonMap, clinical patient data is used. Qualitative results show promising
reconstruction performance of the iRadonMap.
