A nested optimization framework for sound speed imaging and uncertainty estimation in ultrasound computed tomography...

Full-waveform inversion (FWI) for ultrasound computed tomography (USCT) has recently been investigated extensively for high-resolution sound-speed (SS) imaging. However, the nonconvexity of FWI hampers global convergence, yielding limited robustness and artifacts that constrain clinical applicability. Existing methods often struggle to balance computational efficiency with robustness, or require extensive hyperparameter tuning. Furthermore, uncertainty estimation for SS imaging in USCT has attracted growing interest, but existing methods remain insufficiently analyzed and validated through in vivo experiments. To address these limitations, we propose a physics-driven nested-optimized FWI framework that decomposes each iteration into two cascaded modules-sound-speed optimization and regularization updating-utilizing a Mamba-based neural network as a learnable regularizer. The framework employs a shot-splitting strategy to enable efficient, purely physics-driven updates of both SS and the network. We further incorporate a group random sampling scheme to facilitate uncertainty estimation. To validate the proposed method, we conducted numerical simulations, phantom studies, in vivo experiments on breast and musculoskeletal datasets, and comparison experiments with magnetic resonance imaging. Quantitative evaluations on the two datasets with homogeneous initial model demonstrate that the proposed method consistently outperforms the best-performing baseline, reducing the mean learned perceptual image patch similarity by up to 8.24% and improving the mean contrast-normalized root mean square error and structural similarity index measure by up to 22.65% and 2.46%, respectively. In phantom and in vivo experiments, it suppresses cycle-skipping artifacts and resolves in vivo micro-structures down to 0.767 mm. Furthermore, it reduces imaging time by 73.5% compared to other implicit regularization-based FWI methods and yields uncertainty maps correlated with reconstruction errors distribution for image quality assessment.