Nonlinear Microwave Imaging for Breast-Cancer Screening Using Gauss-Newton's Method and the CGLS Inversion Algorithm

• Published in: IEEE transactions on antennas and propagation Vol. 55; no. 8; pp. 2320 - 2331
• Main Authors: Rubaek, Tonny, Meaney, Paul M., Meincke, Peter, Paulsen, Keith D.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.08.2007; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied classical electromagnetism; Applied sciences; Biomedical electromagnetic imaging; Breast cancer; cancer; Diffraction, scattering, reflection; electromagnetic scattering inverse problems; Electromagnetic wave propagation, radiowave propagation; Electromagnetism; electron and ion optics; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Gauss-Newton method; Gaussian processes; image reconstruction; imaging; inverse problems; Inversions; Iterative algorithms; Least squares methods; Mathematical analysis; Microwave imaging; Microwave theory and techniques; Microwaves; Newton method; nonlinear equations; Nonlinearity; Optical imaging; Physics; Radiocommunications; Radiowave propagation; Recursive estimation; Screening; Studies; Telecommunications; Telecommunications and information theory; X-ray imaging; Breast disease; Image processing; Gauss Newton method; Updating; Iterative method; Jacobi matrix; Image reconstruction; Microwave measurement; Least squares method; inverse problems; Tomography; Biomedical imaging; Microwave imaging; Electromagnetic wave scattering; Conjugate gradient method; electromagnetic scattering inverse problems; Electromagnetism; Biomedical electromagnetic imaging; Mammography; Nonlinear problems; Malignant tumor; Algorithm; imaging; Inverse problem; Image quality; nonlinear equations; Electromagnetic wave propagation; Wave scattering; Medical imagery; cancer
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2007.901993

Breast-cancer screening using microwave imaging is emerging as a new promising technique as a supplement to X-ray mammography. To create tomographic images from microwave measurements, it is necessary to solve a nonlinear inversion problem, for which an algorithm based on the iterative Gauss-Newton method has been developed at Dartmouth College. This algorithm determines the update values at each iteration by solving the set of normal equations of the problem using the Tikhonov algorithm. In this paper, a new algorithm for determining the iteration update values in the Gauss-Newton algorithm is presented which is based on the conjugate gradient least squares (CGLS) algorithm. The iterative CGLS algorithm is capable of solving the update problem by operating on just the Jacobian and the regularizing effects of the algorithm can easily be controlled by adjusting the number of iterations. The new algorithm is compared to the Gauss-Newton algorithm with Tikhonov regularization and is shown to reconstruct images of similar quality using fewer iterations.