Fast Jacobian Matrix Formulation for Microwave Tomography Applications

We have developed a new technique for computing the Jacobian matrix for microwave tomography systems which is orders of magnitude faster than conventional approaches. It exploits concepts from the nodal adjoint method and previous observations that rows of the matrix can be plotted over the imaging domain to produce sensitivity maps associated with specific transmit/receive antenna pairs. It also requires that the forward solutions and parameter reconstruction distributions be represented on the same grid or mesh. In this way, it computes full rows of the matrix simultaneously via a simple vector-vector multiplication of the forward solutions associated with sources broadcasting from both the designated transmit and receive antennas times a scalar constant. The time savings is substantial and is viable for both 2D and 3D applications.