Reconstruction Quality and Spectral Content of an Electromagnetic Time-Domain Inversion Algorithm

Abstract

A tomographic time-domain reconstruction algorithm for solving the inverse electromagnetic problem is described. The application we have in mind is dielectric breast cancer detection but the results are of general interest to the field of microwave tomography. Reconstructions have been made from experimental and numerically simulated data for objects of different sizes in order to investigate the relation between the spectral content of the illuminating pulse and the quality of the reconstructed image. We have found that the spectral content is crucial for a successful reconstruction. The work has further shown that when imaging objects with different scale lengths it is an advantage to use a multiple step procedure. Low frequency content in the pulse is used to image the large structures and the reconstruction process then proceed by using higher frequency data to resolve small scale lengths. Good agreement between the results obtained from experimental data and simulated data has been achieved.

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

“…Qualitative approaches also have been proposed, more recently, for breast cancer imaging, including ultra-wideband synthetic focusing techniques [7][8][9] and a linear sampling technique [10]. Since the nineties quantitative reconstruction algorithms based on rigorous solutions of Maxwell's equations have been developed to provide images of the complex permittivity profile, see, e.g., [11][12][13][14][15][16] for 2D and [13,[16][17][18][19] for 3D frequency-domain techniques and [20][21][22] for time-domain (TD) techniques. 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.…”

“…Since the nineties quantitative reconstruction algorithms based on rigorous solutions of Maxwell's equations have been developed to provide images of the complex permittivity profile, see, e.g., [11][12][13][14][15][16] for 2D and [13,[16][17][18][19] for 3D frequency-domain techniques and [20][21][22] for time-domain (TD) techniques. 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].…”

Extraction of Internal Spatial Features of Inhomogeneous Dielectric Objects Using Near-Field Reflection Data

“…However, the breast has a complicated structure, leading to significant variability in the propagation speed of the electromagnetic energy travelling through tissue. Microwave tomography reconstructs the dielectric properties of an object by using an objective function to measure the discrepancy between the measurements and fields generated by a numerical simulation of the system (i.e., a forward solver) [9][10][11]. The complex nature of the internal breast structure, the lack of a priori information about the internal structure, and limitations in the quality and quantity of the measurement data lead to an inverse scattering problem that is nonlinear, non-convex, and severely ill-posed.…”

Three-Dimensional Reconstruction From Time-Domain Electromagnetic Waves

“…Various inversion methods in the frequency domain [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and time domain [15][16][17][18][19][20][21] that are suitable for large-size and high-contrast objects have been developed in the last twenty years. For the frequency domain methods there are Born and distorted Born iterative method, Newton-Kantorovitch method, contrast source and modified contrast source inversion method, local shape function method, etc.…”