A new formulation of the probe method and related problems

Abstract

The probe method gives a general idea to obtain a reconstruction formula of unknown objects embedded in a known background medium from a mathematical counterpart (the Dirichlet-to-Neumann map) of the measured data of some physical quantity on the boundary of the medium. It is based on the sequence of special solutions of the governing equation for the background medium related to a singular solution of the equation. In this paper the blowup property of the sequence is clarified. Moreover a new formulation of the probe method based on the property is given in some typical inverse boundary value problems.