The third annual special session on image reconstruction using real data. 2. The application of back-propagation algorithms to the Ipswich data: preliminary results

For pt.1 see ibid., vol.41, no.1, p.34-51 (1999). The Ipswich data provide a unique opportunity for the validation of the approximate back-propagation (ABP) methods, which were originally developed to identify the shape of acoustic scatterers in the resonance region. These methods rely on a heuristic relationship, i.e., ABP, between the expansion coefficients that represent the scattered wave in the far zone and those on the obstacle boundary, Γ. The unknown is the shape-parameter vector, ψ&oarr;∈Ψ_ad, the admissible set. The objective function to be minimized is the L² (Γ)-norm of the boundary defect. In the vertical-polarization case, ABP consists of an affine map, which is easy to derive. Its ingredients are arrays of inner products in L²(Γ), where outgoing cylindrical wave functions are involved. The corresponding numerical results, based on the IPS001VV data, are satisfactory. The attraction domain of the expected solution, the reference obstacle (a disk), is numerically determined by varying the initial conditions in a wide subset of Ψ_ad. Reconstruction seems to be unique, although no uniqueness condition is known for the obstacle. In the horizontal-polarization case, ABP relies on vector harmonic functions in a cylindrical geometry. The complexity of the algorithm is higher. Results based on the TPS001HH set are summarized. Although the numerical solution does not show any focal minimum other than the reference obstacle, the corresponding attraction domain is smaller than in the vertical-polarization case