Data-driven volumetric reconstruction for optically measured sound field using physics-constrained 3D Gaussian splatting

Acousto-optic sensing is a powerful approach to measuring sound at a high resolution; yet, it faces a critical challenge because the measured value is a line integral of the sound. To solve this problem, sound-field reconstruction methods have been proposed. Promising approaches include physical-model-based reconstruction methods, which represent a sound field as a linear combination of basis functions and determine the expansion coefficients. However, they are limited by the choice of basis functions, which means that each model has a suitable sound field, making it difficult to apply a single model to all sound fields. In this paper, a data-driven approach that is applicable to high-complexity sound fields is proposed. A 3D Gaussian splatting (3DGS) scheme for three-dimensional (3D) sound-field reconstruction is leveraged. 3DGS is an advanced and cutting-edge approach in computer vision, which represents a 3D scene as the sum of Gaussian kernels placed in 3D space. In the proposed method, the 3DGS-based volume reconstruction approach, R2-Gaussian, is expanded to handle arbitrary real numbers to represent sound fields and introduces a Helmholtz loss in the optimization. Evaluation experiments were performed with 11 simulated sound fields and 1 measured sound field. The experiments have revealed that the 3DGS-based approach can reconstruct sound fields.