Microwave tomographic imaging of the breast for cancer detection is a topic of considerable interest because of the potential to exploit the apparent high-dielectric property contrast between normal and malignant tissue. An important component in the realization of an imaging system is the antenna array to be used for signal transmission/detection. The monopole antenna has proven to be useful in our implementation because it can be easily and accurately modeled and can be positioned in close proximity to the imaging target with high-element density when configured in an imaging array. Its frequency response is broadened considerably when radiating in the liquid medium that is used to couple the signals into the breast making it suitable for broadband spectral imaging. However, at higher frequencies, the beam patterns steer further away from the desired horizontal plane and can cause unwanted multipath contributions when located in close proximity to the liquid/air interface. In this paper, we have studied the behavior of these antennas and devised strategies for their effective use at higher frequencies, especially when positioned near the surface of the coupling fluid which is used. The results show that frequencies in excess of 2 GHz can be used when the antenna centers are located as close as 2 cm from the liquid surface.

We introduce the discrete dipole approximation (DDA) for efficiently calculating the two-dimensional electric field distribution for our microwave tomographic breast imaging system. For iterative inverse problems such as microwave tomography, the forward field computation is the time limiting step. In this paper, the two-dimensional algorithm is derived and formulated such that the iterative conjugate orthogonal conjugate gradient (COCG) method can be used for efficiently solving the forward problem. We have also optimized the matrix-vector multiplication step by formulating the problem such that the nondiagonal portion of the matrix used to compute the dipole moments is block-Toeplitz. The computation costs for multiplying the block matrices times a vector can be dramatically accelerated by expanding each Toeplitz matrix to a circulant matrix for which the convolution theorem is applied for fast computation utilizing the fast Fourier transform (FFT). The results demonstrate that this formulation is accurate and efficient. In this work, the computation times for the direct solvers, the iterative solver (COCG), and the iterative solver using the fast Fourier transform (COCG-FFT) are compared with the best performance achieved using the iterative solver (COCG-FFT) in C++. Utilizing this formulation provides a computationally efficient building block for developing a low cost and fast breast imaging system to serve under-resourced populations.