Ultrasonic Medical Tissue Imaging Using Probabilistic Inversion: Leveraging Variational Inference for Speed Reconstruction and Uncertainty Quantification

Full Waveform Inversion (FWI) is a promising technique for achieving high-resolution imaging in medical ultrasound. However, conventional FWI methods suffer from issues related to computational efficiency, dependence on initial models, and the inability to quantify uncertainty. This study aims to enhance inversion performance and provide a reliable method for uncertainty quantification in medical FWI imaging. This study integrates the Stein Variational Gradient Descent (SVGD) algorithm into the FWI framework by deriving the posterior gradient for probabilistic inversion. To evaluate the proposed method, numerical experiments are conducted on synthetic datasets, including a breast tissue model with realistic anatomical structure. Imaging accuracy and uncertainty quantification are assessed to compare the performance of SVGD-based FWI with conventional FWI and Stochastic Variational Inference (SVI) methods. Markov Chain Monte Carlo (MCMC) is implemented as a benchmark to evaluate the quality of uncertainty estimates. For synthetic data, the SVGD-based FWI framework yields more precise estimates in the region of interest (ROI) and demonstrates faster convergence compared to the conventional FWI. For the anatomically realistic breast tissue simulation, SVGD produces a maximum relative error of 1.10\% and a mean relative error of 0.09\% in the ROI. The estimated uncertainty is spatially consistent, with most values below 0.01 and a mean of approximately 0.003. Compared to SVI, SVGD provides improved structural resolution and stronger agreement with the MCMC benchmark, indicating more reliable uncertainty quantification. The SVGD-based FWI method improves inversion quality, enhances uncertainty quantification. These findings indicate that probabilistic inversion is a promising tool for addressing the limitations of traditional FWI methods in ultrasonic imaging of medical tissues.