A Subspace Preconditioned LSQR Gauss-Newton Method with a Constrained Line Search Path Applied to 3D Biomedical Microwave Imaging
Three contributions that can improve the performance of a Newton-type iterative quantitative microwave imaging algorithm in a biomedical context are proposed. (i) To speed up the iterative forward problem solution, we extrapolate the initial guess of the field from a few field solutions correspondin...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | International Journal of Antennas and Propagation |
| Online Access: | http://dx.doi.org/10.1155/2015/924067 |
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| author | Jürgen De Zaeytijd Ann Franchois |
| author_facet | Jürgen De Zaeytijd Ann Franchois |
| author_sort | Jürgen De Zaeytijd |
| collection | DOAJ |
| description | Three contributions that can improve the performance of a Newton-type iterative quantitative microwave imaging algorithm in a biomedical context are proposed. (i) To speed up the iterative forward problem solution, we extrapolate the initial guess of the field from a few field solutions corresponding to previous source positions for the same complex permittivity (i.e., “marching on in source position”) as well as from a Born-type approximation that is computed from a field solution corresponding to one previous complex permittivity profile for the same source position. (ii) The regularized Gauss-Newton update system can be ill-conditioned; hence we propose to employ a two-level preconditioned iterative solution method. We apply the subspace preconditioned LSQR algorithm from Jacobsen et al. (2003) and we employ a 3D cosine basis. (iii) We propose a new constrained line search path in the Gauss-Newton optimization, which incorporates in a smooth manner lower and upper bounds on the object permittivity, such that these bounds never can be violated along the search path. Single-frequency reconstructions from bipolarized synthetic data are shown for various three-dimensional numerical biological phantoms, including a realistic breast phantom from the University of Wisconsin-Madison (UWCEM) online repository. |
| format | Article |
| id | doaj-art-a70d8f351bcb4c49ab3a0440abbd64ac |
| institution | OA Journals |
| issn | 1687-5869 1687-5877 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Antennas and Propagation |
| spelling | doaj-art-a70d8f351bcb4c49ab3a0440abbd64ac2025-08-20T02:20:11ZengWileyInternational Journal of Antennas and Propagation1687-58691687-58772015-01-01201510.1155/2015/924067924067A Subspace Preconditioned LSQR Gauss-Newton Method with a Constrained Line Search Path Applied to 3D Biomedical Microwave ImagingJürgen De Zaeytijd0Ann Franchois1Department of Information Technology (INTEC), Ghent University, Sint-Pietersnieuwstraat 41, 9000 Gent, BelgiumDepartment of Information Technology (INTEC), Ghent University, Sint-Pietersnieuwstraat 41, 9000 Gent, BelgiumThree contributions that can improve the performance of a Newton-type iterative quantitative microwave imaging algorithm in a biomedical context are proposed. (i) To speed up the iterative forward problem solution, we extrapolate the initial guess of the field from a few field solutions corresponding to previous source positions for the same complex permittivity (i.e., “marching on in source position”) as well as from a Born-type approximation that is computed from a field solution corresponding to one previous complex permittivity profile for the same source position. (ii) The regularized Gauss-Newton update system can be ill-conditioned; hence we propose to employ a two-level preconditioned iterative solution method. We apply the subspace preconditioned LSQR algorithm from Jacobsen et al. (2003) and we employ a 3D cosine basis. (iii) We propose a new constrained line search path in the Gauss-Newton optimization, which incorporates in a smooth manner lower and upper bounds on the object permittivity, such that these bounds never can be violated along the search path. Single-frequency reconstructions from bipolarized synthetic data are shown for various three-dimensional numerical biological phantoms, including a realistic breast phantom from the University of Wisconsin-Madison (UWCEM) online repository.http://dx.doi.org/10.1155/2015/924067 |
| spellingShingle | Jürgen De Zaeytijd Ann Franchois A Subspace Preconditioned LSQR Gauss-Newton Method with a Constrained Line Search Path Applied to 3D Biomedical Microwave Imaging International Journal of Antennas and Propagation |
| title | A Subspace Preconditioned LSQR Gauss-Newton Method with a Constrained Line Search Path Applied to 3D Biomedical Microwave Imaging |
| title_full | A Subspace Preconditioned LSQR Gauss-Newton Method with a Constrained Line Search Path Applied to 3D Biomedical Microwave Imaging |
| title_fullStr | A Subspace Preconditioned LSQR Gauss-Newton Method with a Constrained Line Search Path Applied to 3D Biomedical Microwave Imaging |
| title_full_unstemmed | A Subspace Preconditioned LSQR Gauss-Newton Method with a Constrained Line Search Path Applied to 3D Biomedical Microwave Imaging |
| title_short | A Subspace Preconditioned LSQR Gauss-Newton Method with a Constrained Line Search Path Applied to 3D Biomedical Microwave Imaging |
| title_sort | subspace preconditioned lsqr gauss newton method with a constrained line search path applied to 3d biomedical microwave imaging |
| url | http://dx.doi.org/10.1155/2015/924067 |
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