Interpretable wavelet transformer-enhanced framework for unsupervised deformable image registration

Deformable image registration (DIR) underpins quantitative analysis in clinical image-based diagnosis and intervention. Nevertheless, prevailing techniques falter due to their inadequate capacity to encapsulate high-frequency multi-scale data. Additionally, they lack explicit constraints on the deformation learning process, leading to poor interpretability.

To address these challenges, we propose WaveMorph, a DIR framework enhanced by discrete wavelet Transformers.

The WaveMorph framework is composed of wavelet-based modules, characterized by their explicitly interpretable mathematical formulations. Specifically, we designed the Discrete Wavelet Transformer (DWFormer) module for the encoder, which helps capture high-frequency multi-scale details and enables information-preserving feature encoding. We also devised the Inverse Wavelet Transform Up-sampling (IWTU) enhanced decoder, which accumulates high-frequency multi-scale information from the encoder for precise reconstruction of the displacement vector field using a coarse-to-fine approach.

Comparative and ablation experiments were conducted on publicly available datasets, including OASIS, IXI, LPBA40, and MMWHS. Compared to state-of-the-art (SOTA) methods such as TransMorph, TransMatch, and UTSRMorph, our proposed method demonstrated superior performance.

The experimental results show that the wavelet transformer-based network is effective in deformable MRI registration due to its ability to capture multi-scale features and its strong interpretability.