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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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