RNN-Based Full Waveform Inversion for Robust Multi-Parameter Bone Quantitative Imaging

The full waveform inversion (FWI) method plays a significant role in bone quantitative imaging. It is shown that even a small deviation in transducer positions can lead to a considerable variation in frequency-domain signals, and result in a marked decline in the performance of frequency-domain full waveform inversion (FDFWI). To address this limitation, a multi-parameter time-domain full waveform inversion algorithm based on a recurrent neural network (RNN-MPTDFWI) is proposed for bone quantitative imaging.

In the proposed method, a variable-density acoustic wave equation which takes sound velocity and bone density as parameters is solved in the time domain within RNN cells as the forward model. Multiscale inversion is conducted with filtered signals iteratively from low to high frequency bands via minimizing a misfit function between the simulated and observed data. Automatic differentiation for multi-parameter gradient calculation and adaptive momentum estimation (Adam) algorithm are utilized in the optimization process. After the estimated velocity and density are obtained, bone images are generated based on these parameters.

Numerical simulation results demonstrate that RNN-MPTDFWI reduces the mean relative errors (MREs) of the reconstructed velocity and density by at least 54.56% and 71.64%, respectively, compared to FDFWI.

These improvements highlight that RNN-MPTDFWI offers more accurate representations of bone geometry and microarchitecture, along with enhanced robustness against transducer position errors.