Masked Wavelet Scattering Transform Neural Field for Sound Field Reconstruction

In this paper, we propose a reconstruction framework that leverages the Wavelet Scattering Transform (WST) as a multi-scale feature extractor to impose statistical priors under sparse observation conditions. The reconstruction problem is formulated as an optimization task and solved using a neural field, with the WST incorporated into the training loss function. As a proof of concept, we validate the proposed method on HRTF upsampling. A masking strategy is applied to the WST coefficients, resulting in a two-phase procedure. The first phase learns a binary mask from a small multi-subject dataset, while the second phase applies the learned mask to the WST coefficients of an individual HRTF to preserve informative statistical structures during reconstruction. Validation against baseline methods, which also serve as an ablation study of the different components of the framework, demonstrates the effectiveness of the proposed approach.

Differentiable physics for sound field reconstruction

Sound field reconstruction involves estimating sound fields from a limited number of spatially distributed observations. This work introduces a differentiable physics approach for sound field reconstruction, where the initial conditions of the wave equation are approximated with a neural network, and the differential operator is computed with a differentiable numerical solver. The use of a numerical solver enables a stable network training while enforcing the physics as a strong constraint, in contrast to conventional physics-informed neural networks, which include the physics as a constraint in the loss function. We introduce an additional sparsity-promoting constraint to achieve meaningful solutions even under severe undersampling conditions. Experiments demonstrate that the proposed approach can reconstruct sound fields under extreme data scarcity, achieving higher accuracy and better convergence compared to physics-informed neural networks.