Sobolev space norm regularized full waveform inversion for ultrasound computed tomography

Full waveform inversion (FWI) is a complex data fitting process based on full wavefield modeling, aiming to quantitatively reconstruct unknown model parameters from partial waveform data with high-resolution. However, this process is highly nonlinear and ill-posed, therefore achieving high-resolution imaging of complex biological tissues within a limited number of iterations remains challenging. We propose a multiscale frequency–domain full waveform inversion (FDFWI) framework for ultrasound computed tomography (USCT) imaging of biological tissues, which innovatively incorporates Sobolev space norm regularization for enhancement of prior information. Specifically, we investigate the effect of different types of hyperparameter on the imaging quality, during which the regularization weight is dynamically adapted based on the ratio of the regularization term to the data fidelity term. This strategy reduces reliance on predefined hyperparameters, ensuring robust inversion performance. The inversion results from both numerical and experimental tests (i.e., numerical breast, thigh, and ex vivo pork-belly tissue) demonstrate the effectiveness of our regularized FWI strategy. These findings will contribute to the application of the FWI technique in quantitative imaging based on USCT and make USCT possible to be another high-resolution imaging method after x-ray computed tomography and magnetic resonance imaging.