3D Fresnel Volumizing for Efficient Implicit Velocity Field Reconstruction

Reconstructing velocity distributions using wavefield responses provides a powerful tool for probing the internal structures of objects and has been widely applied in nondestructive testing, geological exploration, and medical imaging. While full waveform inversion (FWI) provides high-resolution results, its severe ill-posedness and high computational cost hinder efficient 3D reconstruction. In this paper, we propose a novel framework for efficient 3D internal velocity field reconstruction. First, we parameterize the velocity field with a coordinate-based neural network as an implicit continuous function, enabling compact representation from sparse observations. Second, we adopt ray-based traveltime tomography with multi-level parallel forward modeling to accelerate computation. Third, we introduce a differentiable Fresnel volumizing method that extends 1D ray paths into 3D volumetric regions (i.e., Fresnel volumes), enabling spatially continuous and multi-scale gradient diffusion, thus alleviating gradient sparsity and improving reconstruction accuracy. To further improve efficiency, we propose a 2D slice-based construction of 3D Fresnel volumes using a lightweight neural network. Extensive experiments on synthetic datasets, including ablation studies, demonstrate up to 10 times speedup over FWI while maintaining comparable accuracy, validating the effectiveness of the proposed method for efficient 3D inverse problems.