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International Journal of Antennas and Propagation
Volume 2019, Article ID 9014969, 12 pages
https://doi.org/10.1155/2019/9014969
Research Article

A Discrete Dipole Approximation Solver Based on the COCG-FFT Algorithm and Its Application to Microwave Breast Imaging

1Electrical Engineering Department, Chalmers University of Technology, 41296 Gothenburg, Sweden
2The Thayer School of Engineering, Dartmouth College, Hanover, NH 03755, USA

Correspondence should be addressed to Samar Hosseinzadegan; es.sremlahc@hramas

Received 26 February 2019; Revised 6 May 2019; Accepted 20 May 2019; Published 17 July 2019

Guest Editor: Sandra Costanzo

Copyright © 2019 Samar Hosseinzadegan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.