Optimal trajectory design for moving-sensor modal reconstruction

Determine which sensor trajectory minimizes modal reconstruction error subject to a specified path-length or duration budget, and establish the theoretical and empirical performance of trajectory-based sensing for recovering modal amplitudes from spatially distributed temporal samples.

Background

The paper identifies compact-array aperture as a structural limitation: adding microphones within a small fixed aperture does not provide sufficient spatial diversity for recovering many modal amplitudes. It proposes moving a compact sensor array through the domain as an alternative, thereby generating additional effective spatial samples over time.

A sufficiently mixing trajectory may recover the eigenfunction orthogonality properties needed for the isotropy argument, but the paper does not determine how to choose such a trajectory optimally or validate the resulting method. The authors explicitly defer the trajectory formulation, its theory, and its empirical validation to future work.

References

Optimality questions, such as what trajectory minimizes the reconstruction error subject to a path-length or duration budget, become the natural subject of follow-up work. We leave the trajectory formulation, its theoretical analysis, and its empirical validation to that paper.

— Why Learning Rediscovers the Closed-Form Diagonal Regularizer  (2609.09656 - Han et al., 9 Sep 2026) in Appendix, Section “Resolution via distributed temporal sampling”