Scattered Field Data Research Articles

A Hybrid Quantitative Method for Inverse Scattering of Multiple Dielectric Objects

A hybrid method is proposed to locate the boundaries and determine the dielectric constants of multiple homogeneous scatterers by postprocessing the results of the linear sampling method (LSM). The hybrid method is composed of three steps combining the capabilities of the LSM, the multiple signal classification (MUSIC) algorithm, and the generalized multipole technique (GMT). Initially, a new measure of the noise level of the multistatic response (MSR) matrix is proposed. Subsequently, the LSM is applied using the Tikhonov regularization. Then, the scattered field is back-propagated into the investigation domain using the GMT, where in order to ensure the stability, a MUSIC-based approach is exploited to determine the optimum reconstructing multipole sources. The case of limited scattered field data is also addressed by introducing a modification of the Papoulis–Gerchberg algorithm (PGA). Finally, the boundary and the dielectric constant of each scatterer are obtained simultaneously by solving an inverse boundary value problem through an optimization. The proposed hybrid approach is capable of efficiently approximating the dielectric constant of multiple homogeneous dielectric scatterers in a parallel manner. The effectiveness of the proposed method and the accuracy of the solutions are demonstrated by applying the method to both numerical and measured data.

3D MICROWAVE TOMOGRAPHY WITH HUBER REGULARIZATION APPLIED TO REALISTIC NUMERICAL BREAST PHANTOMS

Quantitative active microwave imaging for breast cancer screening and therapy monitoring applications requires adequate reconstruction algorithms, in particular with regard to the nonlinearity and ill-posedness of the inverse problem. We employ a fully vectorial three-dimensional nonlinear inversion algorithm for reconstructing complex permittivity profiles from multi-view single-frequency scattered field data, which is based on a Gauss-Newton optimization of a regularized cost function. We tested it before with various types of regularizing functions for piecewise-constant objects from Institut Fresnel and with a quadratic smoothing function for a realistic numerical breast phantom. In the present paper we adopt a cost function that includes a Huber function in its regularization term, relying on a Markov Random Field approach. The Huber function favors spatial smoothing within homogeneous regions while preserving discontinuities between contrasted tissues. We illustrate the technique with 3D reconstructions from synthetic data at 2GHz for realistic numerical breast phantoms from the University of Wisconsin-Madison UWCEM online repository: we compare Huber regularization with a multiplicative smoothing regularization and show reconstructions for various positions of a tumor, for multiple tumors and for different tumor sizes, from a sparse and from a denser data configuration.

Classification of underwater targets from autonomous underwater vehicle sampled bistatic acoustic scattered fields.

One of the long term goals of autonomous underwater vehicle (AUV) minehunting is to have multiple inexpensive AUVs in a harbor autonomously classify hazards. Existing acoustic methods for target classification using AUV-based sensing, such as sidescan and synthetic aperture sonar, require an expensive payload on each outfitted vehicle and post-processing and/or image interpretation. A vehicle payload and machine learning classification methodology using bistatic angle dependence of target scattering amplitudes between a fixed acoustic source and target has been developed for onboard, fully autonomous classification with lower cost-per-vehicle. To achieve the high-quality, densely sampled three-dimensional (3D) bistatic scattering data required by this research, vehicle sampling behaviors and an acoustic payload for precision timed data acquisition with a 16 element nose array were demonstrated. 3D bistatic scattered field data were collected by an AUV around spherical and cylindrical targets insonified by a 7-9 kHz fixed source. The collected data were compared to simulated scattering models. Classification and confidence estimation were shown for the sphere versus cylinder case on the resulting real and simulated bistatic amplitude data. The final models were used for classification of simulated targets in real time in the LAMSS MOOS-IvP simulation package [M. Benjamin, H. Schmidt, P. Newman, and J. Leonard, J. Field Rob. 27, 834-875 (2010)].

Scattering Centers Induced by Creeping Waves on Cone-Shaped Targets in Bistatic Mode

The scattering center induced by creeping waves on cone-shaped targets in bistatic mode is investigated in this communication. This scattering center shows significant signatures in bistatic radar images, and could be classified as a distributed scattering center, i.e., this scattering center can only be observed at narrow aspect looks, and with a certain length of distribution. The relations of the distribution and the observable aspect looks with the factors, such as the bistatic angle, the orientations of target relative to radar, and the geometry of the target, are derived in this communication. The analytical conclusions about the scattering center have been well validated by the scattered field characteristics, the image signatures in the time-frequency representations, and the range profiles of radar echoes from the target. As an important scattering feature of cone-shaped targets, an approach using this scattering center to extract motion and geometric parameters has been further explored; the performance of this approach are validated by simulations. To assure the accuracy and reliability of simulations, scattered field data in simulations are computed by the well-validated full-wave numerical method (FE-BI-MLFMA).

Experimental Validation of the Quadratic Forward Model for RF Tomography

An effective way to solve the inverse scattering from dielectric objects relies on the Born approximation, which allows to linearize the problem and retrieve a qualitative reconstruction of the targets in terms of location and extent. The limits of the validity of the linear model can be extended by considering a quadratic approximation of the operator relating the scattered field data to the unknown object function. The use of the quadratic operator allows on the one hand to recover additional spatial variations of the object profile and on the other hand to mitigate the local minima (false solution) problem typically affecting nonlinear inversion methods. In this letter, we present an experimental validation of the quadratic inverse model for dielectric objects in free space. The data processing confirms that the tomographic images based on the quadratic model are better resolved compared to the ones provided by the inversion of the linear Born model.

Analysis of MUSIC-type imaging functional for single, thin electromagnetic inhomogeneity in limited-view inverse scattering problem

This study analyzes the well-known MUltiple SIgnal Classification (MUSIC) algorithm to identify unknown support of thin penetrable electromagnetic inhomogeneity from scattered field data collected within the so-called multi-static response matrix in limited-view inverse scattering problems. The mathematical theories of MUSIC are partially discovered, e.g., in the full-view problem, for an unknown target of dielectric contrast or a perfectly conducting crack with the Dirichlet boundary condition (Transverse Magnetic–TM polarization) and so on. Hence, we perform further research to analyze the MUSIC-type imaging functional and to certify some well-known but theoretically unexplained phenomena. For this purpose, we establish a relationship between the MUSIC imaging functional and an infinite series of Bessel functions of integer order of the first kind. This relationship is based on the rigorous asymptotic expansion formula in the existence of a thin inhomogeneity with a smooth supporting curve. Various results of numerical simulation are presented in order to support the identified structure of MUSIC. Although a priori information of the target is needed, we suggest a least condition of range of incident and observation directions to apply MUSIC in the limited-view problem.

An extended diffraction tomography method for quantifying structural damage using numerical Green’s functions

Existing damage imaging algorithms for detecting and quantifying structural defects, particularly those based on diffraction tomography, assume far-field conditions for the scattered field data. This paper presents a major extension of diffraction tomography that can overcome this limitation and utilises a near-field multi-static data matrix as the input data. This new algorithm, which employs numerical solutions of the dynamic Green’s functions, makes it possible to quantitatively image laminar damage even in complex structures for which the dynamic Green’s functions are not available analytically. To validate this new method, the numerical Green’s functions and the multi-static data matrix for laminar damage in flat and stiffened isotropic plates are first determined using finite element models. Next, these results are time-gated to remove boundary reflections, followed by discrete Fourier transform to obtain the amplitude and phase information for both the baseline (damage-free) and the scattered wave fields. Using these computationally generated results and experimental verification, it is shown that the new imaging algorithm is capable of accurately determining the damage geometry, size and severity for a variety of damage sizes and shapes, including multi-site damage. Some aspects of minimal sensors requirement pertinent to image quality and practical implementation are also briefly discussed.

Scattering Centers Induced by Creeping Waves on Streamlined Cone-Shaped Targets in Bistatic Mode

Scattering centers induced by creeping waves on streamlined cone-shaped targets in bistatic radar mode have been investigated in this letter. The scattering center slides on the smooth surface of the target with the change of radar aspect angles and shows significant feature in bistatic radar images. Based on the geometrical theory of diffraction, the equivalent location of the sliding scattering center has been deduced by tracing the diffraction rays on the streamlined surface. A mathematical model for this sliding scattering center has been further proposed in order to precisely describe the bistatic scattering characteristics of these targets. The parameters of the model are directly related with the geometry of the target and the bistatic angle bisector of the radar, which is significant for the application of using scattering center model in geometry and motion parameters extraction from radar echoes. The analysis of the scattering center has been validated by the scattering data and the time-frequency representations (TFRs) of the bistatic radar echoes from two streamlined targets. The scattered field data are computed by the well-validated full-wave numerical method (FE-BI-MLFMA) to assure the reliability of the validation.

3D Imaging of Dielectric Objects Buried under a Rough Surface by Using CSI

A 3D scalar electromagnetic imaging of dielectric objects buried under a rough surface is presented. The problem has been treated as a 3D scalar problem for computational simplicity as a first step to the 3D vector problem. The complexity of the background in which the object is buried is simplified by obtaining Green’s function of its background, which consists of two homogeneous half-spaces, and a rough interface between them, by using Buried Object Approach (BOA). Green’s function of the two-part space with planar interface is obtained to be used in the process. Reconstruction of the location, shape, and constitutive parameters of the objects is achieved by Contrast Source Inversion (CSI) method with conjugate gradient. The scattered field data that is used in the inverse problem is obtained via both Method of Moments (MoM) and Comsol Multiphysics pressure acoustics model.

Reconstruction of three-dimensional targets using frequency-diversity data

In this paper, we consider the imaging of targets with a multi-frequency microwave experiment and investigate the best way to take advantage of the frequency-diversity data for reconstructing the three-dimensional permittivity of the objects from the scattered field data. We derive two inversion procedures where the permittivity is estimated iteratively so as to minimize an adequate cost functional. In the first approach, known as the frequency hopping procedure, the inversion scheme is run on a single frequency dataset, starting from the lowest frequency, and its final result is used as an initial guess for the inversion performed on the next frequency dataset. In the second approach, the inversion procedure is applied to the full multi-frequency data. We show on various targets taken from the Fresnel database, that the best reconstructions are obtained when the inversion procedure acts on the full data. The reconstruction can be further ameliorated by modifying the weight of the different frequencies in the cost functional.

Microwave medical imaging based on sparsity and an iterative method with adaptive thresholding.

We propose a new image recovery method to improve the resolution in microwave imaging applications. Scattered field data obtained from a simplified breast model with closely located targets is used to formulate an electromagnetic inverse scattering problem, which is then solved using the Distorted Born Iterative Method (DBIM). At each iteration of the DBIM method, an underdetermined set of linear equations is solved using our proposed sparse recovery algorithm, IMATCS. Our results demonstrate the ability of the proposed method to recover small targets in cases where traditional DBIM approaches fail. Furthermore, in order to regularize the sparse recovery algorithm, we propose a novel L(2) -based approach and prove its convergence. The simulation results indicate that the L(2)-regularized method improves the robustness of the algorithm against the ill-posed conditions of the EM inverse scattering problem. Finally, we demonstrate that the regularized IMATCS-DBIM approach leads to fast, accurate and stable reconstructions of highly dense breast compositions.

Inhomogeneity reconstructions in tendon ducts via boundary integral equations

In this study, as an alternative to the formerly presented investigations, Newton-type numerical algorithms are proposed to find location and shape of an air void inside of a tendon duct and to identify gathered metallic bars in a concrete column. The simulated structures are illuminated by four acoustic sources at a fixed frequency such that the scattered field is measured in a near-field region at 128 points. According to the nature of physical problems, the Dirichlet boundary condition is employed to model air-filled cavities and transmission conditions are assumed for metallic objects. Additionally, conductive boundary conditions are suggested for a more realistic representation of the inhomogeneities for the rusty metallic skin of the duct. Potential approaches are used to derive boundary integral equations. The proper treatment of the ill-conditioned equations is established via Tikhonov regularization. Applicability of the proposed inversion algorithms is tested with realistic parameters for different scenarios using noisy scattered field data and accurate numerical results are presented at 10kHz for the unknown physical properties of the duct׳s skin.

Beamforming-Enhanced Inverse Scattering for Microwave Breast Imaging.

We present a focal-beamforming-enhanced formulation of the distorted Born iterative method (DBIM) for microwave breast imaging. Incorporating beamforming into the imaging algorithm has the potential to mitigate the effect of noise on the image reconstruction. We apply the focal-beamforming-enhanced DBIM algorithm to simulated array measurements from two MRI-derived, anatomically realistic numerical breast phantoms and compare its performance to that of the DBIM formulated with two non-focal schemes. The first scheme simply averages scattered field data from reciprocal antenna pairs while the second scheme discards reciprocal pairs. Images of the dielectric properties are reconstructed for signal-to-noise ratios (SNR) ranging from 35 dB down to 0 dB. We show that, for low SNR, the focal beamforming algorithm creates reconstructions that are of higher fidelity with respect to the exact dielectric profiles of the phantoms as compared to reconstructions created using the non-focal schemes. At high SNR, the focal and non-focal reconstructions are of comparable quality.

Weakly convex discontinuity adaptive regularization for 3D quantitative microwave tomography

We present an analysis of weakly convex discontinuity adaptive (WCDA) models for regularizing three-dimensional (3D) quantitative microwave imaging. In particular, we are concerned with complex permittivity reconstructions from sparse measurements such that the reconstruction process is significantly accelerated. When dealing with such a highly underdetermined problem, it is crucial to employ regularization, relying in this case on prior knowledge about the structural properties of the underlying permittivity profile: we consider piecewise homogeneous objects. We present a numerical study on the choice of the potential function parameter for the Huber function and for two selected WCDA functions, one of which (the Leclerc–Cauchy-Lorentzian function) is designed to be more edge-preserving than the other (the Leclerc–Huber function). We evaluate the effect of reducing the number of (simulated) scattered field data on the reconstruction quality. Furthermore, reconstructions from subsampled single-frequency experimental data from the 3D Fresnel database illustrate the effectiveness of WCDA regularization.

Use of supervised machine learning for real-time classification of underwater targets using Autonomous Underwater Vehicle sampled bistatic acoustic scattered fields

A method has been developed for the classification of underwater target geometry using bistatic acoustic amplitude data collected by an Autonomous Underwater Vehicle (AUV) as it follows a selected path through the scattered field created by a fixed source insonifying a target. The mobility of an AUV allows it to exploit features of this field in three dimensions. The classification method presented includes offline and onboard processing components, which use a combination of signal processing, vehicle behaviors, and machine learning in the form of Support Vector Machines (SVMs) to extract target geometry from collected acoustic data. The offline training and analysis step creates training and test vector sets in a selected feature space from existing scattered field data and outputs models for target classification, confidence, and feature ranking. Several algorithms are explored for selecting the feature space used by the SVM. The models produced by the offline processing step are used in the real-time classification processing chain onboard an AUV sampling an unclassified target's scattered field. The presented simulation results use scattered fields modeled using OASES-SCATT and demonstrate real-time processing and path planning in the LAMSS MOOS-IvP simulation environment. [Work supported by ONR Code 321 OA and NSF GRFP.]

Tomographic airborne ground penetrating radar imaging: Achievable spatial resolution and on-field assessment

Ground Penetrating Radar (GPR) airborne systems are gaining an increasing attention as effective monitoring tools capable of underground investigation of wide areas. With respect to this frame, the paper deals with a reconstruction approach specifically designed to image buried targets from airborne gathered scattered field data. The role of the measurement configuration is investigated in order to address the practical problem of how multi-monostatic and multi-frequency data should be gathered, in terms of synthetic aperture length and frequency range, and how the available data affect the achievable reconstruction capabilities. Such an analysis allows us to evaluate the performance of the reconstruction approach in terms of transversal and depth resolution limits. Finally, an experimental validation of the approach is performed by processing real data.

Differential Microwave Imaging for Brain Stroke Followup

This paper deals with the possibility of adopting microwave imaging to continuously monitor a patient after the onset of a brain stroke, with the aim to follow the evolution of the disease, promptly counteract its uncontrolled growth, and possibly support decisions in the clinical treatment. In such a framework, the assessed techniques for brain stroke diagnosis are indeed not suitable to pursue this goal. Conversely, microwave imaging can provide a diagnostic tool able to follow up the disease’s evolution, while relying on a relatively low cost and portable apparatus. The proposed imaging procedure is based on a differential approach which requires the processing of scattered field data measured at different time instants. By means of a numerical analysis dealing with synthetic data generated for realistic anthropomorphic phantoms, we address some crucial issues for the method’s effectiveness. In particular, we discuss the role of patient-specific information and the effect of inaccuracies in the measurement procedure, such as an incorrect positioning of the probes between two different examinations. The observed results show that the proposed technique is indeed feasible, even when a simple, nonspecific model of the head is exploited and is robust against the above mentioned inaccuracies.

Full three-dimensional imaging via ground penetrating radar: assessment in controlled conditions and on field for archaeological prospecting

This paper deals with an advanced microwave tomographic approach capable of providing full 3D images of buried targets from scattered field data gathered by means of Ground Penetrating Radar (GPR) systems. The approach is based on an approximated model of the scattering phenomenon and it is capable of accounting for the vectorial nature of the interactions occurring between electromagnetic waves and probed materials. Moreover, the Truncated Singular Value Decomposition inversion scheme is exploited to solve the involved linear inverse scattering problem in a stable and accurate way. The advantages offered by the full 3D inversion algorithm with respect to a commonly adopted strategy, which produces 3D images by interpolating 2D reconstructions, are assessed against GPR data gathered in laboratory controlled conditions. Moreover, to provide an example of the full 3D imaging capabilities in on field conditions, we report on a GPR measurement campaign carried out at Grotte dell’Angelo, Pertosa, (SA), Southern Italy, one of the most famous sites of the Cilento and Vallo di Diano geopark.

A New Theory of the Generalized Optical Theorem in Anisotropic Media

A new general approach for the generalized optical cross-section theorem and its particular manifestation, the ordinary optical theorem, is developed for electromagnetic scattering in anisotropic media (corresponding to the scatterer and the background medium where the scatterer is embedded). The derived results are based on cross-flux concepts, and interaction and reciprocity relations, and apply under arbitrary incident fields, hence they apply in arbitrary representational domains for the data or scattering matrix. This generalization is demonstrated for arbitrary anisotropic scatterers embedded in lossless anisotropic background media by means of the so-called modified reciprocity theorem plus duality. A new reactive optical theorem is also derived which clarifies the possibilities and limitations of the extraction of reactive energy storage information of an scatterer from scattering field data. Fundamental and practical imaging implications of the derived optical theorems are discussed. The developed theory is elaborated for general anisotropic scatterers embedded in free space via the multipole expansion of the electromagnetic field.

Apposition of the topological sensitivity and linear sampling approaches to inverse scattering

The focus of this study is the reconstruction of a penetrable obstacle in an acoustic medium from the knowledge of incident time-harmonic waves and corresponding scattered fields. The problem is investigated by way of two competing approaches: the method of topological sensitivity and that of linear sampling, that have been successfully developed for a variety of physical settings (acoustic, electromagnetic, elastodynamic) as non-iterative tools for solving the inverse scattering problem. On adopting a particular scattering configuration–plane waves impinging on a spherical obstacle–that permits analytical treatment as the testing platform, a parallel is drawn between the two methods to evaluate their relative performance in reconstructing the obstacle from the scattered field data. For completeness, the comparison is made by considering a range of input parameters in terms of material properties of the scatterer, frequency of illuminating waves, and noise in the data.