Conclusions: The results of this study support the utility of 3-D microwave tomography for imaging the distribution of normal tissues in the breast, specifically, dense fibroglandular tissue versus less dense adipose tissue, and suggest that further investigation of its use for volumetric evaluation of breast density is warranted. © 2010 American Association of Physicists in Medicine. DOI: 10.1118/1.3443569

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Three-dimensional microwave imaging of realistic numerical breast phantoms via a multiple-frequency inverse scattering technique.

Crosshole radar tomography is a useful tool in diverse investigations in geology, hydrogeology, and engineering. Conventional tomograms provided by standard ray-based techniques have limited resolution, primarily because only a fraction of the information contained in the radar data i.e., thefirst-arrivaltimesandmaximumfirst-cycleamplitudesis included in the inversion. To increase the resolution of radar tomograms,wehavedevelopedaversatilefull-waveforminversion scheme that is based on a finite-difference time-domain solution of Maxwell’s equations. This scheme largely accountsforthe3Dnatureofradar-wavepropagationandincludes an efficient method for extracting the source wavelet from the radar data.After demonstrating the potential of the newschemeontworealisticsyntheticdatasets,weapplyitto two crosshole field data sets acquired in very different geologic/hydrogeologic environments. These are the first applications of full-waveform tomography to observed crosshole radar data.The resolution of all full-waveform tomograms is showntobemarkedlysuperiortothatoftheassociatedraytomograms. Small subsurface features a fraction of the dominant radar wavelength and boundaries between distinct geological/hydrological units are sharply imaged in the fullwaveformtomograms.

Application of a new 2D time-domain full-waveform inversion scheme to crosshole radar data

Crosshole radar techniques are important tools for a wide range of geoscientific and engineering investigations. Unfortunately, the resolution of crosshole radar images may be limited by inadequacies of the ray tomographic methods that are commonly used in inverting the data. Since ray methods are based on high-frequency approximations and only account for a small fraction of the information contained in the radar traces, they are restricted to resolving relatively large-scale features. As a consequence, the true potential of crosshole radar techniques has yet to be realized. To address this issue, we introduce a full-waveform inversion scheme that is based on a finite-difference time-domain solution of Maxwell's equations. We benchmark our new scheme on synthetic crosshole data generated from suites of increasingly complex models. The full-waveform tomographic images accurately reconstruct the following: (1) the locations, sizes, and electrical properties of isolated subwavelength objects embedded in homogeneous media; (2) the locations and sizes of adjacent subwavelength objects embedded in homogeneous media; (3) abrupt media boundaries and average and stochastic electrical property variations of heterogeneous layered models; and (4) the locations, sizes, and electrical conductivities of water-filled tunnels and closely spaced subwavelength pipes embedded in heterogeneous layered models. The new scheme is shown to be remarkably robust to the presence of uncorrelated noise in the radar data. Several limitations of the full-waveform tomographic inversion are also identified. For typical crosshole acquisition geometries and parameters, small resistive bodies and small closely spaced dielectric objects may be difficult to resolve. Furthermore, electrical property contrasts may be underestimated. Nevertheless, the full-waveform inversions usually provide substantially better results than those supplied by traditional ray methods.

Full-Waveform Inversion of Crosshole Radar Data Based on 2-D Finite-Difference Time-Domain Solutions of Maxwell's Equations

The detection of early-stage tumors in the breast by microwave imaging is challenged by both the moderate endogenous dielectric contrast between healthy and malignant glandular tissues and the spatial resolution available from illumination at microwave frequencies The high endogenous dielectric contrast between adipose and fibroglandular tissue structures increases the difficulty of tumor detection due to the high dynamic range of the contrast function to be imaged and the low level of signal scattered from a tumor relative to the clutter scattered by normal tissue structures Microwave inverse scattering techniques, used to estimate the complete spatial profile of the dielectric properties within the breast, have the potential to reconstruct both normal and cancerous tissue structures However, the ill-posedness of the associated inverse problem often limits the frequency of microwave illumination to the UHF band within which early-stage cancers have subwavelength dimensions In this computational study, we examine the reconstruction of small, compact tumors in three-dimensional numerical breast phantoms by a multiple-frequency inverse scattering solution Computer models are also employed to investigate the use of exogenous contrast agents for enhancing tumor detection Simulated array measurements are acquired beforeandaftertheintroductionoftheassumedcontrasteffectsfortwospecific agents currently under consideration for breast imaging: microbubbles and carbon nanotubes Differential images of the applied contrast demonstrate the potential of the approach for detecting the preferential uptake of contrast agents by malignant tissues (Some figures in this article are in colour only in the electronic version)

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Contrast-enhanced microwave imaging of breast tumors: a computational study using 3D realistic numerical phantoms

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.

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

Linear inverse scattering method based on the Born approximation has found wide applications in the on-site detection of buried objects, such as in diffraction tomography. However, the Born approximation becomes invalid when the contrast of targets is high, in which the multiple-scattering effect within the target is more important. To avoid solving the nonlinear inverse scattering problem for large-contrast objects, quasi-linear and modified quasi-linear approximations are proposed based on the extended Born approximation. In this paper, new formulations are derived for the inversion of large-contrast dielectric objects buried in a lossy earth using the idea of backconditioner and lumped-mass approximation. We have shown that the zeroth-order form of such formulations is just the well-known Born approximation, and the first-order form is completely equivalent to the extended Born approximation-based quasi-linear approximation. Hence, high-order approximations are proposed in this paper, which are given in closed forms. Using such approximations, good resolution images can be obtained for large-contrast objects by only solving a linear inverse scattering integral equation. Reconstruction examples show the validity and efficiency of the proposed formulae.

http://iopscience.iop.org/article/10.1088/0266-5611/20/6/S04/pdf

Low-frequency detection of two-dimensional buried objects using high-order extended Born approximations

Low-frequency detection of two-dimensional buried objects using high-order extended Born approximations : Electromagnetic characterization of buried obstacles

An efficient inversion method is proposed using Cui et al.'s high-order extended Born approximations to reconstruct the conductivity object function of three-dimensional dielectric objects buried in a lossy Earth. High-order solutions of the object function are obtained, which have closed-form relations to the linear inverse-scattering solution. Because such relations can be evaluated quickly using the fast Fourier transform, the high-order solutions have similar simplicity as the linear inversion. When the contrasts of buried objects are large, the high-order solutions are much more accurate due to the approximate consideration of multiple-scattering effects within the objects. Hence, good-resolution images can be obtained for large-contrast objects using the new method by only solving a linear inverse problem. Numerical experiments have shown the validity and efficiency of the proposed method.

Efficient low-frequency inversion of 3-D buried objects with large contrasts

In this paper, three-dimensional (3D) subsurface imaging by inversion of data obtained from the very early time electromagnetic system (VETEM) is presented. The distorted Born iterative method is used to match the internal nonlinear property of the 3D inversion problem. The frequency explored is from 0.062 to 3.052 MHz, the high end of which is beyond the induction range. No reported 3D approximation works well for this frequency range, thus the 3D stabilized bi-conjugate-gradient fast Fourier transform method is invoked as the forward solver, in which the total current formulation other than the induced current formulation is used to achieve higher stability. With the use of the reciprocity theorem, the Frechet derivatives are computed rapidly by two calls to the forward solver. Tikhonov regularization is used so that the contribution from small singular values is suppressed to warrant a smooth solution. The selection of regularization parameter follows a heuristic rule as used in the Levenberg–Marquardt algorithm so that the iteration is stable. Processing the whole data set at one time is prohibitively time-consuming and expensive. The localized property of the geophysical problem is exploited to decompose the original large problem into a number of smaller subproblems. The nonlinear inversion is implemented subsequently on each subproblem first. The inverted conductivity profiles are then combined together to arrive at a complete conductivity image under the whole data domain. The proposed method is first tested on synthetic data and then applied to the VETEM data from the Pit 9 complex of the Department of Energy.

http://iopscience.iop.org/article/10.1088/0266-5611/20/6/S12/pdf

3D near-to-surface conductivity reconstruction by inversion of VETEM data using the distorted Born iterative method

In this work, new closed-form formulations are derived for the inverse scattering of 2D large-contrast dielectric objects, buried in a lossy earth, using the idea of back-conditioner and lumped-mass approximation. These formulations are also valid to the case of free space. It has been demonstrated that the zeroth-order form of the new approximation is just the well-known Born approximation, and the first-order form is completely equivalent to the quasi-linear approximation. Hence, high-order approximations are proposed in this work for the imaging of buried objects in lossy earth. Reconstruction examples show the validity and efficiency of these formulations.

Gong-Li Wang

Papers

Low-frequency detection of two-dimensional buried objects using high-order extended Born approximations

Low-frequency detection of two-dimensional buried objects using high-order extended Born approximations : Electromagnetic characterization of buried obstacles

Efficient low-frequency inversion of 3-D buried objects with large contrasts

3D near-to-surface conductivity reconstruction by inversion of VETEM data using the distorted Born iterative method

High-order inversion formulas for low-frequency imaging of 2D buried targets