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

The Ipswich data provide a unique opportunity for the validation of the app roximate back-propagation (ABP) methods, which were originally developed to identify the shape of acoustic scatterers in the resonance region. Said me thods rely on a heuristic relationship, i.e., ABP, between the expansion co efficients that represent the scattered wave in the far zone and those on t he obstacle boundary, Gamma. The unknown is the shape-parameter vector, <(p si)over bar> is an element of Psi(ad), the admissible set. The objective fu nction to be minimized is the L-2(Gamma)-norm of the boundary defect. In th e vertical-polarization case, ABP consists of an affine map, which is easy to derive. Its ingredients are arrays of inner products in L-2(Gamma), wher e outgoing cylindrical wave functions are involved. The corresponding numerical results, based on the IPS001VV data, are satisf actory. The attraction domain of the expected solution, the reference obsta cle (a disk), is numerically determined by varying the initial conditions i n a wide subset of Psi(ad). Reconstruction seems to be unique, although no uniqueness condition is known for said obstacle. In the horizontal-polariza tion case, ABP relies on vector harmonic functions in a cylindrical geometr y. The complexity of the algorithm is higher. Results based on the IPS001HH set are summarized. Although the numerical solution does not show any loca l minimum other than the reference obstacle, the corresponding attraction d omain is smaller than in the vertical-polarization case.