  This work highlights the significance of equivariant networks as efficient
and high-performance approaches for tomography applications. Our study builds
upon the limitations of conventional Convolutional Neural Networks (CNNs),
which have shown promise in post-processing various medical imaging systems.
However, the efficiency of conventional CNNs heavily relies on an undiminished
and proper training set. To tackle this issue, in this study, we introduce an
equivariant network, aiming to reduce CNN's dependency on specific training
sets. We evaluate the efficacy of equivariant spherical CNNs (SCNNs) for 2- and
3- dimensional medical imaging problems. Our results demonstrate superior
quality and computational efficiency of SCNNs in denoising and reconstructing
benchmark problems. Furthermore, we propose a novel approach to employ SCNNs as
a complement to conventional image reconstruction tools, enhancing the outcomes
while reducing reliance on the training set. Across all cases, we observe a
significant decrease in computational costs while maintaining the same or
higher quality of image processing using SCNNs compared to CNNs. Additionally,
we explore the potential of this network for broader tomography applications,
particularly those requiring omnidirectional representation.
