A discrete dipole approximation solver based on the COCG-FFT algorithm and its application to microwave breast imaging
Journal article, 2019

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.

Approximation algorithms

Electric fields

Computational efficiency

Computation theory

Conjugate gradient method

Author

Samar Hosseinzadegan

Chalmers, Electrical Engineering, Signalbehandling och medicinsk teknik, Biomedical Electromagnetics

Andreas Fhager

Chalmers, Electrical Engineering, Signalbehandling och medicinsk teknik, Biomedical Electromagnetics

Mikael Persson

Chalmers, Electrical Engineering, Signalbehandling och medicinsk teknik

Paul M Meaney

Thayer School of Engineering at Dartmouth

Chalmers, Electrical Engineering, Signalbehandling och medicinsk teknik, Biomedical Electromagnetics

Sandra Costanzo

University of Calabria

International Journal of Antennas and Propagation

1687-5869 (ISSN) 1687-5877 (eISSN)

Vol. 2019 9014969

Subject Categories

Computer Engineering

Computational Mathematics

Control Engineering

DOI

10.1155/2019/9014969

More information

Latest update

11/27/2019