Multi-stencil fast-marching-based method for three-dimensional image reconstruction in ultrasound computed tomography

Bent-ray model-based ultrasound computed tomography (USCT) relies on numerical solutions of the Eikonal equation. However, as a mainstream solution method in two-dimensional scenarios, the conventional fast marching method (FMM) suffers from limited accuracy in three-dimensional (3D) settings, which degrades the quality of reconstructed sound speed images. In this study, we propose multi-stencil fast marching methods (MSFM) tailored for 3D-USCT reconstruction. MSFM incorporates a second-order finite difference approximation for partial derivatives and a joint solution strategy using four directional stencils that cover the 18-neighborhood of each grid point. This design significantly improves the numerical accuracy of the Eikonal solution and enhances the quality of 3D sound speed image reconstruction. Numerical simulations based on the Shepp-Logan phantom and bronchus phantom demonstrate that, compared with conventional FMM, MSFM reduces the RMSE from 37.62/57.61 to 29.86/30.87 and improves the PSNR from 16.62/12.92 to 18.63/18.34 for the respective phantoms. MSFM enhances reconstructed image quality, effectively suppresses artifacts and noise, while demonstrating the capability to maintain stable convergence during iterative reconstruction processes. The proposed method provides high-precision sound speed maps, supporting applications in breast cancer screening, soft tissue imaging, and potentially enhancing photoacoustic computed tomography reconstruction and multimodal image fusion.