A Discrete Dipole Approximation Solver Based on the COCG-FFT Algorithm and Its Application to Microwave Breast Imaging
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....
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | International Journal of Antennas and Propagation |
| Online Access: | http://dx.doi.org/10.1155/2019/9014969 |
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| author | Samar Hosseinzadegan Andreas Fhager Mikael Persson Paul Meaney |
| author_facet | Samar Hosseinzadegan Andreas Fhager Mikael Persson Paul Meaney |
| author_sort | Samar Hosseinzadegan |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-6512627d2a5743f281dfd94c89111fd5 |
| institution | Kabale University |
| issn | 1687-5869 1687-5877 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Antennas and Propagation |
| spelling | doaj-art-6512627d2a5743f281dfd94c89111fd52025-02-03T01:12:50ZengWileyInternational Journal of Antennas and Propagation1687-58691687-58772019-01-01201910.1155/2019/90149699014969A Discrete Dipole Approximation Solver Based on the COCG-FFT Algorithm and Its Application to Microwave Breast ImagingSamar Hosseinzadegan0Andreas Fhager1Mikael Persson2Paul Meaney3Electrical Engineering Department, Chalmers University of Technology, 41296 Gothenburg, SwedenElectrical Engineering Department, Chalmers University of Technology, 41296 Gothenburg, SwedenElectrical Engineering Department, Chalmers University of Technology, 41296 Gothenburg, SwedenElectrical Engineering Department, Chalmers University of Technology, 41296 Gothenburg, SwedenWe 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.http://dx.doi.org/10.1155/2019/9014969 |
| spellingShingle | Samar Hosseinzadegan Andreas Fhager Mikael Persson Paul Meaney A Discrete Dipole Approximation Solver Based on the COCG-FFT Algorithm and Its Application to Microwave Breast Imaging International Journal of Antennas and Propagation |
| title | A Discrete Dipole Approximation Solver Based on the COCG-FFT Algorithm and Its Application to Microwave Breast Imaging |
| title_full | A Discrete Dipole Approximation Solver Based on the COCG-FFT Algorithm and Its Application to Microwave Breast Imaging |
| title_fullStr | A Discrete Dipole Approximation Solver Based on the COCG-FFT Algorithm and Its Application to Microwave Breast Imaging |
| title_full_unstemmed | A Discrete Dipole Approximation Solver Based on the COCG-FFT Algorithm and Its Application to Microwave Breast Imaging |
| title_short | A Discrete Dipole Approximation Solver Based on the COCG-FFT Algorithm and Its Application to Microwave Breast Imaging |
| title_sort | discrete dipole approximation solver based on the cocg fft algorithm and its application to microwave breast imaging |
| url | http://dx.doi.org/10.1155/2019/9014969 |
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