Uniqueness and stability of the solution to an inverse acoustic scattering problem

The uniqueness and stability of a discrete inverse scattering problem (functional description) is considered. The number of degrees of freedom, which determines the way of sampling for the functions of the scatterer and the secondary sources induced in it, may considerably vary from one problem to another, thus providing the adequacy of the discrete formulation of a specific problem. This number depends on the size of the scattering region in space and on the widths of the spatial spectra of both the scatterer and the secondary sources. Nonuniqueness of the solution occurs because of the configurations of secondary sources that exist in the scattering region and are not observable in any of the experiments. It is shown that precisely the number of degrees of freedom of the secondary sources determines the amount of discrete scattering data that is necessary to provide a unique solution. If this amount is collected in the experiments without exceeding a certain classical limiting resolution, the solution to the inverse problem is unique and stable. (C) 2003 MAIK "Nauka/Interperiodica".