In recent years there has been an increased interest in the use of microwaves in medical imaging,particularly for the detection of cancerous tumors.This method is based on the fact that cancerous tumors have a significantly different index of refraction.Hence,the mathematical problem is basically an inverse scattering problem for electromagnetic waves.We will present a method for determining the support of tumors in the body which is suitable for microwave imaging and leads to the problem of solving an improperly posed Fredholm integral equation of the first kind.We note that the validity of this integral equation is unrestricted,i.e. no physical approximations have been made in its derivation.The investigation of this equation leads to the study of a new class of boundary value problems for elliptic equations called interior transmission problems.Numerical examples using synthethic data will be given showing the potential practicality of our method.

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1996-1997 Mathematics in High Performance Computing