Group equivariant pyramid network for respiratory motion correction on PET image

Respiratory-induced artefacts cause blurring in PET images, impairing lesion identification and diagnosis. Existing correction methods exhibit limited feature learning capabilities, making it challenging to effectively eliminate artefacts.

The authors developed an SE(3)-equivariant convolution for 3D PET medical images. A Group Equivariant Dual-Pyramid Network (GEPN) was constructed, integrating channel-spatial attention-enhanced convolutional neural networks (CNNs) and SE(3) group-equivariant convolutional neural networks (G-CNNs) within its pyramid encoder for efficient organ feature extraction. The decoder proposed a novel Lie group-based motion decomposition strategy: multi-head neighbourhood attention captured inter-organ displacement, while an SE(3)-equivariant head resolved rotational/translational components, jointly mitigating respiratory motion artefacts.

Experimental validation across diverse PET lung datasets demonstrates the superiority of GEPN. The method achieves Dice coefficients of 97.81 % for geometric phantom data, 92.07 % for lung phantom data, and 81.01 % for clinical data. Compared to baseline models, GEPN improves the Dice coefficient by 5.17 %. Furthermore, it exhibits significantly better artefact correction performance than existing methods in terms of lesion clarity and motion pattern alignment.

The GEPN framework successfully addresses respiratory artefact challenges through its innovative integration of group-equivariant architectures and attention mechanisms. Experimental results validate its effectiveness in enhancing PET image quality, outperforming existing approaches in both quantitative and perceptual metrics, thereby offering a robust solution to improve diagnostic reliability in clinical practice.

The GEPN framework provides clinicians with significantly sharper PET images with reduced motion blur, enabling a more precise delineation of tumour boundaries and extent. This enhanced accuracy in defining lesion morphology directly supports improved radiotherapy planning, surgical targeting, and treatment response assessment.