Efficient 2D and 3D electrical impedance tomography using dual reciprocity boundary element techniques

Abstract Numerical algorithms based on boundary element methods are developed for application to problems in Electrical Impedance Tomography (EIT). Two types of EIT problems are distinguished. In the first type internal boundaries of domains of constant conductivity are imaged. For such problems an algorithm based on identifying the shape of the included region is developed, and uses conventional BEM techniques. For problems where a distribution of conductivity is to be imaged algorithms that use dual reciprocity techniques are developed. The size of the inverse problem required to be solved is much reduced, offering substantial speed-ups over conventional techniques. Further, the present algorithms use simple parametrization of the unknowns to achieve efficiency. Numerical results from tests of this algorithm on synthetic data are presented, and these show that the method is quite promising.