Exploiting Symmetry in Electromagnetic Imaging Problems by using Group Representation Theory

Deepak Kumar Ghodgaonkar ; Razidah Ismail

Bulletin of the Malaysian Mathematical Society, Tome 23 (2000) no. 1

Résumé

Electromagnetic Imaging problems involve development of an algorithm for estimation of complex permittivities of a N -cell body from the knowledge of scattered electric fields at N receiver locations, incident electric fields at N -cell centroid locations, cell sizes, cell locations and receiver locations. In this algorithm, it is necessary to invert a scattering matrix, which relates polarization current inside the body to scattered electric fields outside the body. To allow for a large number of cells, it is necessary to reduce matrix formation and inversion time. This is achieved by block diagonalization of the scattering matrix using standard point symmetry groups and . For three planes of symmetry, two planes of symmetry and one plane of symmetry, it is necessary to use groups and , respectively. Group multiplication and character tables for these groups will be discussed. Due to n planes of symmetry which depend on the configuration of the imaging problem regarding cell locations, cell sizes, receiver locations and transmitter location, it is possible to block diagonalize the scattering matrix. In this paper, block diagonalized matrix is derived for one plane of symmetry which can be generalized to two or three planes of symmetry. Because of block diagonalization, it is observed that it is necessary to consider matrices of instead of one scattering matrix. Hence, it is observed that the matrix formation time and storage requirements of the scattering matrix are reduced by a factor and inversion time is reduced by a factor of .