Puyan Mojabi

A Wideband Microwave Tomography System With a Novel Frequency Selection Procedure

In this paper, we describe a 2-D wideband microwave imaging system intended for biomedical imaging. The system is capable of collecting data from 3 to 6 GHz, with 24 coresident antenna elements connected to a vector network analyzer via a 2 × 24 port matrix switch. As one of the major sources of error in the data collection process is a result of the strongly coupling 24 coresident antennas, we provide a novel method to avoid the frequencies where the coupling is large enough to prevent successful imaging. Through the use of two different nonlinear reconstruction schemes, which are an enhanced version of the distorted born iterative method and the multiplicative regularized contrast source inversion method, we show imaging results from dielectric phantoms in free space. The early inversion results show that with the frequency selection procedure applied, the system is capable of quantitatively reconstructing dielectric objects, and show that the use of the wideband data improves the inversion results over single-frequency data.

Comparison of an Enhanced Distorted Born Iterative Method and the Multiplicative-Regularized Contrast Source Inversion method

For 2D transverse magnetic (TM) microwave inversion, multiplicative-regularized contrast source inversion (MR-CSI), and the distorted Born iterative method (DBIM) are compared. The comparison is based on a computational resource analysis, inversion of synthetic data, and inversion of experimentally collected data from both the Fresnel and UPC Barcelona data sets. All inversion results are blind, but appropriate physical values for the reconstructed contrast are maintained. The data sets used to test the algorithms vary widely in terms of the background media, antennas, and far/near field considerations. To ensure that the comparison is replicable, an automatic regularization parameter selection method is used for the additive regularization within the DBIM, which utilizes a fast implementation of the L-curve method and the Laplacian regularizer. While not used in the classical DBIM, we introduce an MR term to the DBIM in order to provide comparable results to MR-CSI. The introduction of this MR term requires only slight modifications to the classical DBIM algorithm, and adds little computational complexity. The results show that with the addition of the MR term in the DBIM, the two algorithms provide very similar inversion results, but with the MR-CSI method providing advantages for both computational resources and ease of implementation.

Overview and Classification of Some Regularization Techniques for the Gauss-Newton Inversion Method Applied to Inverse Scattering Problems

Different regularization techniques used in conjunction with the Gauss-Newton inversion method for electromagnetic inverse scattering problems are studied and classified into two main categories. The first category attempts to regularize the quadratic form of the nonlinear data misfit cost-functional at different iterations of the Gauss-Newton inversion method. This can be accomplished by utilizing penalty methods or projection methods. The second category tries to regularize the nonlinear data misfit cost-functional before applying the Gauss-Newton inversion method. This type of regularization may be applied via additive, multiplicative or additive-multiplicative terms. We show that these two regularization strategies can be viewed from a single consistent framework.

Microwave Biomedical Imaging Using the Multiplicative Regularized Gauss--Newton Inversion

The weighted L2-norm total variation multiplicative regularized Gauss-Newton inversion method, recently developed for inversion of low-frequency deep electromagnetic geophysical measurements, is used for microwave biomedical imaging. This inversion algorithm automatically adjusts the regularization weight and provides edge-preserving characteristics. The accuracy of this method is demonstrated by inverting experimental data of a human forearm and synthetic data taken from brain and breast models, both assuming two-dimensional (2D) transverse magnetic illumination.

On Super-Resolution With an Experimental Microwave Tomography System

The resolution of an experimental microwave tomography (MWT) system is investigated. Using two cylindrical nylon targets and an operating frequency of 5 GHz, a separation resolution of 2 mm, or 1/30 of a wavelength, is achieved. While this resolution is among the highest reported in the literature, it is not a sufficiently robust indicator of the expected resolution obtainable for complex targets, and this is shown with further examples of more complicated targets. However, the basic separation resolution limit obtained is a good way of comparing various aspects of different MWT systems.

Analysis of Incident Field Modeling and Incident/Scattered Field Calibration Techniques in Microwave Tomography

Imaging with microwave tomography systems requires both the incident field within the imaging domain as well as calibration factors that convert the collected data to corresponding data in the numerical model used for inversion. The numerical model makes various simplifying assumptions, e.g., 2-D versus 3-D wave propagation, which the calibration coefficients are meant to take into account. For an air-based microwave tomography system, we study two types of calibration techniques-incident and scattered field calibration-combined with two different incident field models: a 2-D line-source and an incident field from full-wave 3-D simulation of the tomography system. Although the 2-D line-source approximation does not accurately model incident field in our system, the use of scattered field calibration with the 2-D line-source provides similar or better images to incident and scattered field calibration with an accurate incident field. Thus, if scattered field calibration is used, a simple (but inaccurate) incident field is acceptable for our microwave tomography system. While not strictly generalizable, we expect our methodology to be applicable to most other microwave tomography systems.

A Novel Microwave Tomography System Based on the Scattering Probe Technique

In this paper, we introduce a novel microwave tomography system, which utilizes 24 double-layered Vivaldi antennas, each of which is equipped with a diode-loaded printed-wire probe. By biasing the probes diodes, the impedance of the probe is modified, allowing an indirect measurement of the electric field at the probes locations. Each printed-wire probe is loaded with five equally spaced p-i-n diodes, in series. We show that electric field data collected in this way within the proposed tomography system can be used to reconstruct the dielectric properties of an object of interest. Reconstructions for various objects are shown. Although the results are still preliminary, sufficient experimentation has been done to delineate the advantages of such an indirect method of collecting scattered-field data for tomographic imaging purposes.

Enhancement of the Krylov Subspace Regularization for Microwave Biomedical Imaging

Although Krylov subspace methods provide fast regularization techniques for the microwave imaging problem, they cannot preserve the edges of the object being imaged and may result in an oscillatory reconstruction. To suppress these spurious oscillations and to provide an edge-preserving regularization, we use a multiplicative regularizer which improves the reconstruction results significantly while adding little computational complexity to the inversion algorithm. We show the inversion results for a real human forearm assuming the 2-D transverse magnetic illumination and a cylindrical object assuming the 2-D transverse electric illumination.

Enhancement of Gauss–Newton Inversion Method for Biological Tissue Imaging

The multiplicatively regularized Gauss-Newton inversion (GNI) algorithm is enhanced and utilized to obtain complex permittivity profiles of biological objects-of-interest. The microwave scattering data is acquired using a microwave tomography system comprised of 24 co-resident antennas immersed into a saltwater matching fluid. Two types of biological targets are imaged: ex vivo bovine legs and in vivo human forearms. Four different forms of the GNI algorithm are implemented: a blind inversion, a balanced inversion, a shape-and-location inversion, and a novel balanced shape-and-location inversion. The latter three techniques incorporate typical permittivity values of biological tissues as prior information to enhance the reconstructions. In those images obtained using the balanced shape-and-location reconstruction algorithm, the various parts of the tissue being imaged are clearly distinguishable. The reconstructed permittivity values in the bovine leg images agree with those obtained via direct measurement using a dielectric probe. The reconstructed images of the human forearms qualitatively agree with magnetic resonance imaging images, as well as with the expected dielectric values obtained from the literature.

A Multiplicative Regularized Gauss–Newton Inversion for Shape and Location Reconstruction

A multiplicative regularized Gauss-Newton inversion algorithm is proposed for shape and location reconstruction of homogeneous targets with known permittivities. The data misfit cost functional is regularized with two different multiplicative regularizers. The first regularizer is the weighted -norm total variation which provides an edge-preserving regularization. The second one imposes a priori information about the permittivities of the objects being imaged. Using both synthetically and experimentally collected data sets, we show that the proposed algorithm is robust in reconstructing the shape and location of homogeneous targets.