Advanced Fast 3-D Electromagnetic Solver for Microwave Tomography Imaging

Abstract

This paper describes a fast-forward electromagnetic solver (FFS) for the image reconstruction algorithm of our microwave tomography system. Our apparatus is a preclinical prototype of a biomedical imaging system, designed for the purpose of early breast cancer detection. It operates in the 3-6-GHz frequency band using a circular array of probe antennas immersed in a matching liquid; it produces image reconstructions of the permittivity and conductivity profiles of the breast under examination. Our reconstruction algorithm solves the electromagnetic (EM) inverse problem and takes into account the real EM properties of the probe antenna array as well as the influence of the patient's body and that of the upper metal screen sheet. This FFS algorithm is much faster than conventional EM simulation solvers. In comparison, in the same PC, the CST solver takes ~45 min, while the FFS takes ~1 s of effective simulation time for the same EM model of a numerical breast phantom.

An Overview of Microwave Imaging for Breast Tumor Detection

“…28 images out of the total 30 images coincided with medical analysis, and 2 cases were different (false negative-1 and false positive-1). A Fast Forward electromagnetic Solver (FFS) was developed in 2017 to speed up the processing involved in the imaging unit [171]. In 2019, super-resolution effects were analysed for the imaging unit utilizing a truncated singular value decomposition-based approach in the linear (Born approximation) and nonlinear modeling in near-field zone [172].…”

Analysis of the Super‐Resolution Effect on Microwave Tomography

“…Naturally, matrix R br can play the role of the image resolution matrix (Wiggins, ) in the context of microwave imaging. For example, the projection matrix R br can be constructed with the help of matrix B r , which contains r columns of smooth sinc‐like cardinal cubic spline BFs (Simonov et al, ). These functions are centered in the nodes of a coarse rectangular grid with spacing that is equal to the SR and is almost orthogonal.…”

“…The following equation provides the relation between the matrixes R br and B r : where is a dual matrix. Simonov et al () found that the matrix R br provides imaging with a practically constant SR over the inner points of the IZ. However, inside the border layer with thickness surrounding the SR, the boundary of the IZ cuts the PSF, and the SR is not well defined.…”

“…The equivalency concept is especially useful in the general case, in which the multistatic data matrix is sparse, not full. This situation is suitable for the MT system with a plane circular array, which can scan in the horizontal plane, rotating with small‐angle periods (Simonov et al, ), as well as in the vertical direction. In this case, the Tx antennas have many positions, whereas the Rx antennas only have a small number of corresponding positions equal to the amount of array elements.…”

“…The ASR assumes a homogeneous distribution of SR in the IZ and can be modeled, for example, with the help of sinc‐like basis functions (BFs; Simonov et al, ). As far as these BFs are centered in the nodes of the grid with spacing equal to SR, their number is equal to the effective rank of the corresponding image resolution matrix (Wiggins, ).…”