将循环群等变性融入深度学习以实现旋转对称层析成像系统的可靠重建
Incorporating Cyclic Group Equivariance into Deep Learning for Reliable Reconstruction of Rotationally Symmetric Tomography Systems
AI总结：
本文针对旋转对称层析成像系统，提出循环群等变性深度学习重建框架，通过循环旋转等变卷积和正则化提升泛化性与稳定性，减少伪影并改善细节保持。
摘要：
旋转对称性是许多层析成像系统的一个决定性特征，包括计算机断层扫描（CT）和发射型计算机断层扫描（ECT），其中探测器以圆形或周期性旋转配置排列。本研究从硬件诱导的旋转对称性角度重新审视图像重建过程，并引入一种用于基于深度学习重建的循环群等变性框架。具体而言，我们推导出一个数学对应关系，将投影域中的循环旋转与图像域中的离散旋转耦合起来，二者均源于硬件设计中固有的同一循环群。这一见解还揭示了投影空间均匀分布的圆形结构。基于这一原理，我们提供了一种循环旋转等变卷积设计方法以保持投影域对称性，以及一种循环群等变性正则化方法，在整个网络中强制一致的旋转变换。我们进一步将这些模块集成到域变换重建框架中，并使用数字脑模型进行验证，在离散模型上训练，并在更复杂、更真实的模糊变体上测试。结果表明泛化能力和稳定性显著提高，伪影更少，细节保持更好，尤其是在数据分布偏移的情况下。这些发现凸显了循环群等变性作为旋转对称系统中层析重建统一原则的潜力，为数据有限场景提供了一种灵活且可解释的解决方案。
英文摘要：
Rotational symmetry is a defining feature of many tomography systems, including computed tomography (CT) and emission computed tomography (ECT), where detectors are arranged in a circular or periodically rotating configuration. This study revisits the image reconstruction process from the perspective of hardware-induced rotational symmetry and introduces a cyclic group equivariance framework for deep learning-based reconstruction. Specifically, we derive a mathematical correspondence that couples cyclic rotations in the projection domain to discrete rotations in the image domain, both arising from the same cyclic group inherent in the hardware design. This insight also reveals the uniformly distributed circular structure of the projection space. Building on this principle, we provide a cyclic rotation equivariant convolution design method to preserve projection domain symmetry and a cyclic group equivariance regularization approach that enforces consistent rotational transformations across the entire network. We further integrate these modules into a domain transform reconstruction framework and validate them using digital brain phantoms, training on discrete models and testing on more complex and realistic fuzzy variants. Results indicate markedly improved generalization and stability, with fewer artifacts and better detail preservation, especially under data distribution deviation. These findings highlight the potential of cyclic group equivariance as a unifying principle for tomographic reconstruction in rotationally symmetric systems, offering a flexible and interpretable solution for scenarios with limited data.
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