This work highlights the significance of equivariant networks as efficient
and high-performance approaches for tomography applications. Our study builds
upon the limitations of 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 CNNs on spherical signals for tomographic
medical imaging problems. Our results demonstrate superior quality and
computational efficiency of spherical CNNs (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.

本研究探讨了等变网络在断层扫描成像应用中的重要性，通过解决卷积神经网络在医学成像系统后处理中的局限性，引入了一种能够减少对特定训练集依赖的等变网络，并验证了球面信号上球面卷积神经网络 (SCNNs) 在去噪和重建基准问题中的优越质量和计算效率，同时利用 SCNNs 作为传统图像重建工具的补充方法，提高成像结果质量并降低对训练集的依赖，本研究观察到 SCNNs 与 CNNs 相比，在保持相同或更高的图像处理质量的同时，显著降低了计算成本，并初步探索了其在更广泛断层扫描成像应用中的潜能，特别是那些需要全方位表示的应用。