Solution of inverse problems by the method of auxiliary sources (MAS)

It is known that any wave field carrying the energy into infinity must have the centers of radiation, singularities in some area. Otherwise the wave fields value should be everywhere identically equal to zero. In this paper attention is paid to localization of these singularities under assumption that every wave field is determined by its own singularities in a unique fashion. Investigations have shown that these singularities are distributed as a bright centers. For localization of the wave fields singularities the functions describing the converging and diverging waves are used. Based on these concepts and with the help of the method of auxiliary sources (MAS) a simple numerical method for field reconstruction up to its singularities is suggested in order to solve the inverse problems.