Diffusion-model-based approach for inverse problems in optically measured sound field

Optical sound-field imaging, known for its high spatial resolution, measures sound by detecting small variations in the refractive index of air caused by sound, but often suffers from unavoidable noise contamination. Sound-field reconstruction and extrapolation aim to recover complete sound-field information from limited or patched observations. The tasks of denoising, reconstruction, and extrapolation of sound field imaged by optical measurement can all be viewed as sound-field inverse problems. To address these issues, we propose a diffusion-model-based approach for solving sound-field inverse problems, encompassing denoising, noisy sound-field reconstruction, and extrapolation. During the inference phase of the diffusion model, sound-field degradations are introduced into the reverse denoising process, with range-null space decomposition employed as the solver to iteratively recover information from the observed sound field. The proposed method is trained on sound-field datasets generated from numerical acoustics simulations with randomized parameters, without the need for labeled degradations. Numerical experiments demonstrate that our method outperforms existing deep-learning-based approaches in both sound-field denoising and reconstruction tasks, while also achieving effective performance in sound-field extrapolation. Furthermore, in practical experiments, our method successfully denoised and reconstructed the optically measured sound field, exhibiting excellent performance.