Identifying point sources for biharmonic wave equation from the scattered fields at sparse sensors

Abstract This work addresses the reconstruction of point sources for the biharmonic wave equation using scattered fields at sparse sensors. We first present a uniqueness proof establishing complete characterization of point sources in both R 2 and R 3 using multifrequency sparse scattered fields. In particular, a novel Fourier–Funk–Hecke methodology, specifically designed to address analytical complexities arising from the fundamental solution in R 2 , with demonstrated extensions to the Helmholtz equation. Furthermore, we show that a single point source in R 3 can be identified from the scattered fields taken at only four non-coplanar sensors and three frequencies. It is noteworthy that such a result for the Helmholtz equation is still open. Finally, we propose three numerical algorithms validated through extensive computational experiments, confirming both their effectiveness and robustness in sparse measurement scenarios.