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

Abstract EN

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.