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

/pdf/three-dimensional-microwave-imaging-of-realistic-numerical-4kgd7qkm8a.pdf

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

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

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

Breast imaging via microwave tomography involves estimating the distribution of dielectric properties within the patient's breast on a discrete mesh. The number of unknowns in the discrete mesh can be very large for 3-D imaging, and this results in computational challenges. We propose a new approach where the discrete mesh is replaced with a relatively small number of smooth basis functions. The dimension of the tomography problem is reduced by estimating the coefficients of the basis functions instead of the dielectric properties at each element in the discrete mesh. The basis functions are constructed using knowledge of the location of the breast surface. The number of functions used in the basis can be varied to balance resolution and computational complexity. The reduced dimension of the inverse problem enables application of a computationally efficient, multiple-frequency inverse scattering algorithm in 3-D. The efficacy of the proposed approach is verified using two 3-D anatomically realistic numerical breast phantoms. It is shown for the case of single-frequency microwave tomography that the imaging accuracy is comparable to that obtained when the original discrete mesh is used, despite the reduction of the dimension of the inverse problem. Results are also shown for a multiple-frequency algorithm where it is computationally challenging to use the original discrete mesh.

/pdf/three-dimensional-microwave-breast-imaging-dispersive-4djkf7de83.pdf

Three-Dimensional Microwave Breast Imaging: Dispersive Dielectric Properties Estimation Using Patient-Specific Basis Functions

A diffraction tomographic (DT) algorithm has been proposed for detecting three-dimensional (3-D) dielectric objects buried in a lossy ground, using electric dipoles or magnetic dipoles as transmitter and receiver, where the air-earth interface has been taken into account and the background is lossy. To derive closed-form reconstruction formulas, an approximate generalized Fourier transform is introduced. Using this algorithm, the locations, shapes, and dielectric properties of buried objects can be well reconstructed under the low-contrast condition, and the objects can be well detected even when the contrast is high. Due to the use of fast Fourier transforms to implement the problem, the proposed algorithm is fast and quite tolerant to the error of measurement data, making it possible to solve realistic problems. Reconstruction examples are given to show the validity of the algorithm.

Diffraction tomographic algorithm for the detection of three-dimensional objects buried in a lossy half-space

An efficient inverse-scattering algorithm is developed to reconstruct both the permittivity and conductivity profiles of two-dimensional (2D) dielectric objects buried in a lossy earth using the distorted Born iterative method (DBIM). In this algorithm, the measurement data are collected on (or over) the air-earth interface for multiple transmitter and receiver locations at single frequency. The nonlinearity due to the multiple scattering of pixels to pixels, and pixels to the air-earth interface has been taken into account in the iterative minimization scheme. At each iteration, a conjugate gradient (CG) method is chosen to solve the linearized problem, which takes the calling number of the forward solver to a minimum. To reduce the CPU time, the forward solver for buried dielectric objects is implemented by the CG method and fast Fourier transform (FFT). Numerous numerical examples are given to show the convergence, stability, and error tolerance of the algorithm.

Inverse scattering of two-dimensional dielectric objects buried in a lossy earth using the distorted Born iterative method

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Inverse scattering of two-dimensional dielectric objects buried in a lossy earth using the distorted Born iterative method