Microwave Biomedical Data Inversion Using the Finite-Difference Contrast Source Inversion Method

We present a contrast source inversion (CSI) technique which is based on a finite-difference (FD) solver for use in microwave biomedical imaging. The algorithm is capable of inverting complex-permittivity biomedical data sets without the explicit use of a forward solver at each iteration. The FD solver is based in the frequency domain, utilizes perfectly matched layer (PML) boundary conditions, and the stiffness matrix is solved via an LU decomposition and Gaussian elimination. An important feature of the FD-CSI algorithm is that the stiffness matrix associated with the FD solver depends only upon the background medium and frequency, and thus the LU decomposition is only performed once, before the iterative inversion process. Unlike the usual integral equation (IE) based inversion techniques, the FD-CSI algorithm is readily capable of utilizing an arbitrary backarbitrary backgroundground medium for the inversion process.