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

Abstract

Abstract-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.Index Terms-Biomedical electromagnetic imaging, cancer, electromagnetic scattering inverse problems, image reconstruction, imaging, inverse problems, microwave imaging, nonlinear equations.

Random Radiation Source Optimization Method for Microwave Staring Correlated Imaging Based on Temporal-Spatial Relative Distribution Entropy

“…The emitting frequency and array geometry are integratedly designed by optimization method based on TSRDE. Figure 4 shows the recovery images of the five design methods using CGLS algorithm [26]. The radiation source parameters of these design methods are all the same.…”

The Effect of Antenna Incident Field Distribution on Microwave Tomography Reconstruction

“…The first method relies on using antenna array techniques. This can be practical as MWT setups usually utilize co-resident antenna elements ranging from 16 to 64 antennas [7,[16][17][18][19] placed in an imaging chamber. Currently, these antennas are being used individually for illuminating the OI.…”

“…In this example, we use a breast model that has been previously used in [3,16]. As shown in Figures 5(a)-(b), this model consists of three regions: fibroglandular (smallest circle), tumor (medium circle), and fatty (largest circle) tissues.…”

“…As shown in Figures 5(a)-(b), this model consists of three regions: fibroglandular (smallest circle), tumor (medium circle), and fatty (largest circle) tissues. The background medium is chosen to be 23.4 + j18.5 at the frequency of operation, which is 1 GHz (similar to the background medium used for the breast cancer microwave imaging system at Dartmouth College [16]). This numerical model is illuminated by 24 antennas, which are located on a circle of radius 0.1 m. The inversion results for m = 0, 70 are shown in Figures 5(c)-(f).…”

3d Microwave Tomography With Huber Regularization Applied to Realistic Numerical Breast Phantoms

“…These algorithms have been tested with biomedical experimental data, e.g., for various biological phantoms [16,[22][23][24] and a human forearm [16,25,26] in 2D, for plastic rods in saline [27] in pseudo-3D, for a canine thorax [28] in a 3D scalar approximation and for dielectric balls [29] and a pig hind-leg [30] in fully-vectorial 3D. Quantitative imaging of the breast is reported, e.g., employing 2D single-frequency algorithms with synthetic data [26,31] or with phantom and/or clinical data [32][33][34], a 3D single-frequency algorithm in a scalar approximation with synthetic data [35], a 3D TD algorithm with synthetic and phantom data [36], a 3D multiple-frequency vectorial algorithm with synthetic data [37][38][39][40] and 3D single-frequency fully vectorial algorithms with synthetic data [41][42][43] and with single-polarized clinical data [3]. In this paper we consider a 3D single-frequency fully vectorial imaging algorithm.…”