Recovery of the Shape and Location of a Rigid Cylindrical Body from Experimental Scattered Acoustic Field Data

Abstract

The standard method for solving a boundary-identification inverse problem [2] is to generate a cost functional expressing the discrepancy between the actual (simulated or measured) data and what the estimator predicts the scattered field to be for a set of trial location and boundary parameters of the body; the sought-for parameters are then chosen to be those trial parameters which give rise to the minimum of the cost functional. A major difficulty with this approach, rarely alluded-to in previous studies, is that the cost functional often exhibits not one, but many minima so that the procedure cannot provide a unique solution. We exhibit this fact empirically both for real and simulated data estimated by the ICBA, and observe that the distribution of minima follows a regular pattern, which fact suggests that there exists a simple law relating the position of the minima to some or all of the sought-for parameters.