In this paper we investigate the solvability of an ill-posed two-dimensional Fredholm integral equation of the first kind which allows the solutions of distribution type. The problem is first transformed into a well-posed differential-integral equation using output least-squares approach with a regularization of bounded variations. A globally convergent iterative method is proposed and some numerical results are presented. The methodology discussed may be applied for the identification of the boundary shape of the defects of a dielectric material or the interface between different materials.
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