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An LSTM Based Strategy for Data and Model Calibration in Subsurface Electromagnetic Imaging
... For time-domain-induced electromagnetic signals, long short-term memory (LSTM) passes signals step by step via the time series, utilizing gate mechanisms to selectively retain time-domain signal features carrying crucial electrical media information [35,36]. This optimizes feature extraction from time-domain signals, enhancing the neural network model's predictive capability in electromagnetic signal inversion. ...
Utilizing neural network models to inverse time-domain electromagnetic signals enables rapid acquisition of electrical structures, a non-intrusive method widely applied in geological and environmental surveys. However, traditional multi-layer perceptron (MLP) feature extraction is limited, struggling with cases involving complex electrical media with induced polarization effects, thereby limiting the inversion model’s predictive capacity. A graph-topology-based neural network model for strata electrical structure imaging with long-dependency feature extraction was proposed. We employ graph convolutional networks (GCN) for capturing non-Euclidean features like resistivity-thickness coupling and Long Short-Term Memory (LSTM) to capture long-dependency features. The LSTM compensates for GCN’s constraints in capturing distant node relationships. Using case studies with 5-strata and 9-strata resistivity models containing induced polarization effects, compared to traditional MLP networks, the proposed model utilizing time-domain features and graph-topology-based electrical structure extraction significantly improves performance. The mean absolute error in inversion misfit is reduced from 10–20% to around 2–3%.
The quantitative inspection of unknown targets or bodies by means of microwave tomography requires a proper modeling of the field scattered by the structures under test, which in turn depends on several factors related to the adopted antennas and measurement configuration. In this paper, a multifrequency tomographic approach in nonconstant-exponent Lebesgue spaces is enhanced by a preliminary step that processes the measured scattered field with a neural network based on long short-term memory cells. In the considered cases, this approach allows dealing with measurements in three-dimensional settings obtained with non-ideal antennas and measurement points, while retaining a canonical two-dimensional formulation of the inverse problem. The adopted data-driven model is trained with a set of simulations of cylindrical targets performed with a finite-difference time domain method, considering a simplified bistatic measurement configuration as an initial case study. The inversion procedure is then validated with numerical simulations involving cylindrical and spherical structures.
Ground penetrating radar (GPR) technology for underground exploration consists in the transmission of an electromagnetic signal in the ground for sensing the presence of buried objects. While monostatic or bistatic configurations are usually adopted, a limited number of multistatic GPR systems have been proposed in the scientific literature. In this manuscript, we investigate the recovery performance of a specific and unconventional contactless multistatic GPR system, designed at the Georgia Institute of Technology for the subsurface imaging of anti-tank and anti-personnel plastic mines. In particular, for the first time, tomographic approaches are tested against this experimental multistatic GPR system, while most GPR processing in the scientific literature processes multi-monostatic experimental data sets. Firstly, by mimicking the system at hand, an accurate theoretical as well as numerical analysis is performed in order to estimate the data information content and the performance achievable. Two different tomographic linear approaches are adopted, i.e. the linear sampling method (LSM) and the Born approximation (BA) method, this latter enhanced by means of the compressive sensing (CS) theoretical framework. Then, the experimental data provided by the Georgia Institute of Technology are processed by means of a multi-frequency CS and BA-based method, thus generating very accurate 3D maps of the investigated underground scenario.
gprMax is open source software that simulates electromagnetic wave propagation, using the Finite-Difference Time-Domain (FDTD) method, for the numerical modelling of Ground Penetrating Radar (GPR). gprMax was originally developed in 1996 when numerical modelling using the FDTD method and, in general, the numerical modelling of GPR were in their infancy. Current computing resources offer the opportunity to build detailed and complex FDTD models of GPR to an extent that was not previously possible. To enable these types of simulations to be more easily realised, and also to facilitate the addition of more advanced features, gprMax has been redeveloped and significantly modernised. The original C-based code has been completely rewritten using a combination of Python and Cython programming languages. Standard and robust file formats have been chosen for geometry and field output files. New advanced modelling features have been added including: an unsplit implementation of higher order Perfectly Matched Layers (PMLs) using a recursive integration approach; diagonally anisotropic materials; dispersive media using multi-pole Debye, Drude or Lorenz expressions; soil modelling using a semi-empirical formulation for dielectric properties and fractals for geometric characteristics; rough surface generation; and the ability to embed complex transducers and targets.
Several variants of the Long Short-Term Memory (LSTM) architecture for
recurrent neural networks have been proposed since its inception in 1995. In
recent years, these networks have become the state-of-the-art models for a
variety of machine learning problems. This has led to a renewed interest in
understanding the role and utility of various computational components of
typical LSTM variants. In this paper, we present the first large-scale analysis
of eight LSTM variants on three representative tasks: speech recognition,
handwriting recognition, and polyphonic music modeling. The hyperparameters of
all LSTM variants for each task were optimized separately using random search
and their importance was assessed using the powerful fANOVA framework. In
total, we summarize the results of 5400 experimental runs (about 15 years of
CPU time), which makes our study the largest of its kind on LSTM networks. Our
results show that none of the variants can improve upon the standard LSTM
architecture significantly, and demonstrate the forget gate and the output
activation function to be its most critical components. We further observe that
the studied hyperparameters are virtually independent and derive guidelines for
their efficient adjustment.
A new near-field radar modeling approach for wave propagation in planar layered media is presented. The radar antennas are intrinsically modeled using an equivalent set of infinitesimal electric dipoles and characteristic, frequency-dependent, global reflection, and transmission coefficients. These coefficients determine through a plane wave decomposition wave propagation between the radar reference plane, point sources, and field points. The interactions between the antenna and layered medium are thereby inherently accounted for. The fields are calculated using 3-D Green's functions. We validated the model using an ultrawideband frequency-domain radar with a transmitting and receiving Vivaldi antenna operating in the range 0.8–4 GHz. The antenna characteristic coefficients are obtained from near- and far-field measurements over a copper plane. The proposed model provides unprecedented accuracy for describing near-field radar measurements collected over a water layer, the frequency-dependent electrical properties of which were described using the Debye model. Layer thicknesses could be retrieved through full-wave inversion. The proposed approach demonstrated great promise for nondestructive testing of planar materials and digital soil mapping using ground-penetrating radar.
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 deep-learning (DL)-based data calibration technique applied to quantitative microwave inverse-scattering analysis is presented. This technique aims at subsurface inspection for the buried object under a concrete road or soil. The inverse-scattering analysis provides a complex permittivity profile, which is useful for object identification such as air gap or water. Contrast source inversion (CSI) is one of the most promising inverse-scattering methods. This method is capable of avoiding the iterative use of highly computational forward solvers. However, when applied to the measured data, an appropriate calibration capable of converting measured data to simulation data is required. In this work, a DL-based calibration suitable for nonlinear inverse problems is proposed. Its efficiency is experimentally demonstrated using a concrete cylinder containing water with different salinities.
This work assesses a hybrid calibration technique
that uses together measured and simulated data to compensate
modeling errors such as fabrication tolerances and positioning
inaccuracies. Here, as a proof-of-concept, it is considered a
virtual microwave imaging experiment of a human brain stroke
condition. The test involves a full-wave software based on the
finite element method and 3-D highly realistic system models,
including a set of 24 monopoles immersed in a solid brickshaped
matching medium and a single-cavity anthropomorphic
head phantom. The studied case shows that under favorable
assumptions, the calibration procedure improves the quality
of the retrieved images compared to the non-calibrated-kernel
approach.
A hybrid inversion procedure for subsoil prospecting by ground penetrating radar (GPR) measurements is proposed and experimentally validated in this letter. The approach integrates the benefits of qualitative beamforming in an adaptive multifrequency inexact-Newton scheme formulated in Lebesgue spaces with variable exponents. After a first preprocessing step aimed at estimating the incident field, a delay-and-sum method provides an initial image of the region of interest. Then, the inexact-Newton algorithm exploits the qualitative indicator for both setting the exponent function and selectively weighting the update of the unknown during iterations. The proposed approach is tested against experimental GPR data.
An iterative multiscaling approach for solving the electromagnetic inverse scattering problem related to the imaging of shallow subsurface targets with the ground-penetrating radar (GPR) is proposed. The approach combines the zooming properties of the multiscaling technique with the reconstruction capabilities of an Inexact-Newton (IN) method developed in Lp spaces. It is based on multifrequency processing that allows one to face the ill-posedness of the inverse scattering problem by exploiting the regularization properties of a truncated Landweber (LW) method. Experimental data, extracted from radargrams obtained by the GPR in a real situation, are used for validation. The reconstruction results are also compared with those from competitive alternatives, such as a standard IN method or a state-of-the-art multifrequency Conjugate Gradient (CG)-based approach.
Take-Home Messages • This work deals with the use of microwave imaging (MWI) for brain stroke monitoring and presents a validation of an MWI prototype by means of a high-fidelity numerical model. • The numerical analysis reported in the paper shows that the considered MWI system is capable of performing the monitoring of hemorrhages and clots. • The paper deals with continuous monitoring of brain stroke, which is still an unmet clinical need which cannot be performed with currently adopted imaging modalities like magnetic resonance imaging (MRI) and computerized x-ray tomography (CT). • The main claim of the work is to show how the adoption of a high-fidelity device-specific numerical model is important to perform in silico experiments of complex scenarios needed to address subsequent experimental activities. Abstract-This work presents the outcomes of a numerical analysis based on a 3-D high fidelity model of a realistic microwave imaging system for the clinical follow-up of brain stroke. The analysis is meant as a preliminary step towards the full experimental characterization of the system, with the aim of assessing the achievable results and highlight possible critical points. The system consists of an array of twenty-four printed monopole antennas, placed conformal to the upper part of the head; each monopole is immersed into a semi-solid dielectric brick with custom permittivity, acting as coupling medium. The whole system, including the antennas and their feeding mechanism, has been numerically modeled via a custom full-wave software based on the finite element method. The numerical model generates reliable electromagnetic operators and accurate antenna scattering parameters, which provide the input data for the implemented imaging algorithm. In particular, the numerical analysis assesses the capability of the device of reliably monitoring the evolution of hemorrhages and ischemias, considering the progression from a healthy state to an early-stage stroke.
Stroke identification by means of microwave tomography requires a very accurate reconstruction of the dielectric properties inside patient's head. This is possible when a precise measurement system is combined with a full nonlinear inversion method. In this article, the inversion of S-parameter data collected in a metallic chamber is performed with a nonlinear inversion strategy in Lebesgue spaces with nonconstant exponents. This is the first time that this kind of nonlinear S-parameter electromagnetic formulation has been applied to this problem. The inverse-scattering method incorporates a 2-D electromagnetic model of the imaging chamber based on a finite-element formulation, which has led to a complete redefinition of the solving procedure with respect to previous works. This allows a suitable description of the multistatic S-parameters due to the interactions between the incident radiation and the structure under test. The developed inversion procedure is first assessed by means of numerical simulations. The experimental results, obtained with a clinical microwave system prototype containing a liquid-filled 3-D SAM phantom with an inhomogeneity mimicking a hemorrhagic stroke, further prove the effectiveness of the proposed approach.
When sounding pavement layers using ground penetrating radar (GPR), antenna effects including dispersion and multiple reflections usually degrade the vertical resolution. In far-field conditions, these effects can be analytically filtered out by a linear method. However, for near-field operation, the antenna model tends to be nonlinear, and thus, these unwanted effects cannot be analytically removed anymore. In this letter, a method based on the radial basis function (RBF) neural network is proposed to filter out antenna effects under near-field conditions. A well-developed GPR model is used to simulate the input training data, and the corresponding zero-offset Green's function is calculated as the desired output for each training data. The trained RBF network is applied to the simulated and measured data. The results show that the proposed method is effective in filtering out the antenna effects and increasing the vertical resolution of GPR.
Brain strokes are one of the leading causes of disability and mortality in adults in developed countries. Ischemic stroke (85% of total cases) and hemorrhagic stroke (15%) must be treated with opposing therapies, and thus, the nature of the stroke must be determined quickly in order to apply the appropriate treatment. Recent studies in biomedical imaging have shown that strokes produce variations in the complex electric permittivity of brain tissues, which can be detected by means of microwave tomography. Here, we present some synthetic results obtained with an experimental microwave tomography-based portable system for the early detection and monitoring of brain strokes. The determination of electric permittivity first requires the solution of a coupled forward-inverse problem. We make use of massive parallel computation from domain decomposition method and regularization techniques for optimization methods. Synthetic data are obtained with electromagnetic simulations corrupted by noise, which have been derived from measurements errors of the experimental imaging system. Results demonstrate the possibility to detect hemorrhagic strokes with microwave systems when applying the proposed reconstruction algorithm with edge preserving regularization.
An innovative nonlinear inverse scattering approach in variable exponent Lebesgue spaces is proposed for microwave imaging purposes. The main objective of the approach is to overcome one of the main problems associated to reconstruction procedures developed in Lebesgue spaces with constant exponent, i.e., the need for the selection of the optimum Lebesgue-space norm parameter, which is critical for obtaining accurate reconstructions, and no exact rules exist for this choice. The approach proposed in this paper is oriented to tomographic imaging applications at microwave frequencies, for which the adopted inversion procedure is based on a Gauss-Newton method, which has been reformulated in the unconventional variable exponent Lebesgue spaces. The capabilities of the approach are demonstrated by a set of numerical simulations, in which cylindrical dielectric targets are inspected. Moreover, an experimental result is reported. IEEE
In this paper, we present the results of a whole-system modeling of a microwave measurement prototype for brain imaging, consisting of 160 ceramic-loaded antennas working around 1 GHz. The modelization has been performed using open source FreeFem++ solver. Quantitative comparisons were performed using commercial software Ansys-HFSS and measurements. Coupling effects between antennas are studied with the empty system (without phantom) and simulations have been carried out with a fine numerical brain phantom model issued from scanner and MRI data for determining the sensitivity of the system in realistic configurations.
We introduce Adam, an algorithm for first-order gradient-based optimization
of stochastic objective functions. The method is straightforward to implement
and is based an adaptive estimates of lower-order moments of the gradients. The
method is computationally efficient, has little memory requirements and is well
suited for problems that are large in terms of data and/or parameters. The
method is also ap- propriate for non-stationary objectives and problems with
very noisy and/or sparse gradients. The method exhibits invariance to diagonal
rescaling of the gradients by adapting to the geometry of the objective
function. The hyper-parameters have intuitive interpretations and typically
require little tuning. Some connections to related algorithms, on which Adam
was inspired, are discussed. We also analyze the theoretical convergence
properties of the algorithm and provide a regret bound on the convergence rate
that is comparable to the best known results under the online convex
optimization framework. We demonstrate that Adam works well in practice when
experimentally compared to other stochastic optimization methods.
Multifrequency microwave tomography in Lebesgue spaces with nonconstant exponents
- A Fedeli
- C Estatico
- A Randazzo
- M Pastorino
Multifrequency microwave tomography in Lebesgue spaces with nonconstant exponents
- fedeli