Rigorous sufficiency of point-source near-field data

Establish whether point-source measurements alone, without dipole excitations and normal-derivative measurements, are sufficient to uniquely and rigorously reconstruct an impenetrable clamped obstacle for the biharmonic Helmholtz scattering problem.

Background

The theoretical factorization framework uses multistatic near-field data generated by both point sources and dipoles, together with measurements of the scattered fields and their normal derivatives. Numerical experiments, however, indicate that reconstructions can remain accurate when only point-source scattered-field measurements are used. The unresolved issue is to weaken the analytical data assumptions and prove that point-source data alone provide sufficient information for rigorous obstacle reconstruction. The authors also identify extension to other boundary conditions, including free plate obstacles, as part of the broader future-work direction, but the explicit gap most directly stated here concerns the sufficiency of point-source data.