Wavelet Swin Transformer low-frequency prediction for ultrasound full waveform inversion of bone

Full waveform inversion (FWI) for bone imaging is frequently hindered by local minima arising from insufficient low-frequency energy due to limited transducer bandwidth. This study develops a deep learning framework to predict missing low-frequency information from band-limited high-frequency observations, thereby improving the initialization and stability of frequency-continuation FWI.

We propose a novel Wavelet Swin Transformer (WST) architecture for low-frequency signal prediction. This design integrates Discrete Wavelet Transform (DWT) to decompose high-frequency temporal signals into multi-band wavelet coefficients, effectively capturing both temporal sequence patterns and frequency-domain characteristics. The framework employs a shifted window-based self-attention mechanism to model the intricate spatial and cross-scale dependencies among these coefficients. By employing a shifted window scheme with cyclic shifting, the WST facilitates cross-window information interaction, effectively establishing the non-linear mapping from high-frequency wavefield features to their corresponding low-frequency components.

WST was evaluated using CT-derived human tibia and fibula models. Numerical experiments show that WST significantly outperforms the standard Swin Transformer, reducing velocity RMSE by approximately 45% compared to the baseline. Furthermore, the method maintains superior reconstruction stability under 10 dB noise conditions.

This study demonstrates that WST virtually extends the usable frequency range of band-limited observations by predicting missing low-frequency information from the available high-frequency data. By reducing reliance on additional low-frequency excitation, WST provides a useful foundation for stable bone FWI and quantitative imaging.