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International Journal of Antennas and Propagation
Volume 2015 (2015), Article ID 924067, 21 pages
Research Article

A Subspace Preconditioned LSQR Gauss-Newton Method with a Constrained Line Search Path Applied to 3D Biomedical Microwave Imaging

Department of Information Technology (INTEC), Ghent University, Sint-Pietersnieuwstraat 41, 9000 Gent, Belgium

Received 19 December 2014; Accepted 24 March 2015

Academic Editor: Amelie Litman

Copyright © 2015 Jürgen De Zaeytijd and Ann Franchois. 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.


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.