Author: Fang-Fang Yin, Lei Zhang, Yaogong Zhang 👨🔬
Affiliation: Medical Physics Graduate Program, Duke Kunshan University 🌍
Purpose: Rotational symmetry is an inherent property of many tomography systems (e.g., CT, PET, SPECT), arising from the circular arrangement or rotation of detectors. This study revisits the image reconstruction process from the perspective of hardware-induced symmetry and introduces a cyclic group equivariance framework for deep learning-based reconstruction with enhanced interpretability and generalizability.
Methods: We establish 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. Building on this principle, we proposed a cyclic rotation equivariant convolutional (CREC) layer to preserve projection domain symmetry and a cyclic group equivariance regularization (CGER) approach that enforces consistent rotational transformations across the entire network. These modules were further integrated into a domain transform reconstruction framework AUTOMAP. Experiments were conducted using BrainWeb phantoms and their corresponding simulated sinograms. Discrete anatomical models were used for training, while three types of fuzzy models with more complex and realistic pixel distributions were employed to evaluate generalization performances in real-world scenarios.
Results: The results demonstrate the effectiveness of both CREC layers and CGER constraint in improving model generalization and stability under challenging fuzzy phantom conditions. On the three fuzzy phantoms, introducing CREC layers to the original AUTOMAP significantly enhanced performance, with SSIM gains of 0.0431, 0.0508, and 0.1042, alongside PSNR improvements of 2.25 dB, 3.25 dB, and 3.54 dB, by mitigating blurring and artifacts. The addition of CGER constraints further enforced global symmetry, achieving larger SSIM improvements of 0.1553, 0.1680, and 0.1862, effectively suppressing artifacts and enhancing reconstruction quality.
Conclusion:This study introduces cyclic group equivariance to incorporate hardware-level rotational symmetry into reconstruction network design and optimization, demonstrating its significant role in enhancing both interpretability and generalizability. It provides principled guidance for developing more reliable deep learning-based reconstruction techniques.