Wave-Reg: full-stage wavelet-guided image registration framework with cross-scale correction.

Objective.Complicated deformation remains a critical challenge in medical image registration (MIR). Although deep learning-based spatial domain registration networks have achieved improved accuracy and efficiency, they still suffer from irreversible information loss, the 'small objects move fast' problem-where small objects are lost at low resolutions and reappear with large motions at finer resolutions-and accumulated deformation errors propagating through coarse-to-fine architectures.Approach.We propose Wave-Reg, a spatial-frequency registration framework built on a wavelet pyramid architecture. By integrating the discrete wavelet transform (DWT), the encoder extracts spatial-frequency features via DWT-guided ConvNet to minimize detail loss, while the decoder reconstructs displacement vector field (DVF) via inverse DWT-guided Swin Transformer to mitigate the 'small objects move fast' problem. A cross-scale self-correction module based on Heun's predictor-corrector method further refines deformation fields across scales to tackle accumulated errors.Main results.Experiments on three datasets demonstrate substantial gains in registration accuracy for both large deformation and multi-modality registration tasks.Significance.Wave-Reg demonstrates that spatial-frequency feature learning and predictor-corrector refinement offer an effective solution to longstanding challenges in MIR.