Physics-constrained inverse acoustic reconstruction via POCS-inspired relaxed projection-prox iterations

Abstract

The recovery of the physically missing portion of a coherent acoustic field within a contiguous shadow zone remains a challenging inverse problem when an otherwise measured aperture contains a large masked region. Conventional geometric interpolants rely on smoothness priors that suppress oscillatory Helmholtz structure inside such gaps. We propose a training-free physics-constrained inverse solver based on POCSinspired relaxed projection-prox iterations, in which data consistency is coupled to a soft spectral physics operator rather than a hard projection onto a dispersion manifold. The workflow estimates an active frequency set directly from the available measurements, supports confidence-weighted data updates for noisy sensors, and uses surrogate-gap tuning together with residual-based stopping. For known obstacles, the same framework admits a geometry-aware scattered-field refinement after the free-space completion step. Across representative shadow-gap benchmarks, the method reconstructs masked-region oscillatory structure more faithfully than the tested geometric interpolants and representative physics-based inverse baselines. Within the tested synthetic benchmark regime, these results support the method as a training-free numerical approach for wave-consistent completion of occluded acoustic apertures.