Adaptive sampling for optimized sensor placement in sound field reconstruction

Sound field reconstruction estimates a continuous acoustic field from limited measurements. Yet, sensor placement is often handled by non-adaptive methods (prior designs) that suit spatially stationary fields but can be inefficient for nonstationary sound fields. Within a Bayesian/Gaussian process framework, we first analyze standard non-adaptive criteria (entropy, mutual information, Bayesian Cramér–Rao bound, and transductive experimental design), clarifying equivalences and their geometric consequences—most notably farthest-point tendencies that yield space-filling coverage. Motivated by these insights, we propose an adaptive sampling (AS) strategy that selects sensors sequentially, where leave-one-out cross-validation targets high-error regions (exploitation), whereas a wavelength-based spacing rule (minimum λ/4) maintains global coverage (exploration) and prevents clustering. In simulations, AS matches space-filling designs on stationary fields and substantially improves efficiency on nonstationary fields; for the same normalized mean square error, AS uses about half as many sensors, in terms of the median, as non-adaptive methods. These results indicate that AS can substantially improve the efficiency of sensor placement in practical, sequential measurement workflows.