Permittivity Reconstruction Research Articles

Reconstruction of flame permittivity distribution based on ECT and Lp regularized D-bar method

Abstract The measurement of flame permittivity is significant in obtaining the combustion state. A method of Lp regularized D-bar is proposed in this article, which is used to reconstruct flame permittivity distribution by electrical capacitance tomography (ECT). Firstly, the distribution characteristic of flame permittivity is analyzed using the electric probe method. The simulation model of ECT flame measurement is set up based on the result of flame permittivity distribution. Then, the relationship model between the truncation radius of the D-bar algorithm and noise level is fitted based on the simulation reconstruction results of flame permittivity. The truncation radius of the D-bar algorithm for flame permittivity reconstruction is obtained by the relationship model. The Lp regularization is introduced into the scattering transformation solving of the D-bar algorithm, and the simulation results of flame permittivity reconstruction under different p-values are compared. In the experiment, the reconstruction of flame permittivity by the D-bar algorithm with different truncation radii is compared. The experimental results verify the truncation radius strategy based on noise level. Moreover, compared with L1 and L2 regularization methods, Lp regularization combined with the D-bar algorithm is more accurate in the experiment results of flame permittivity reconstruction.

MR-based electrical property tomography using a physics-informed network at 3 and 7 T.

Magnetic resonance electrical propert tomography promises to retrieve electrical properties (EPs) quantitatively and non-invasively in vivo, providing valuable information for tissue characterization and pathology diagnosis. However, its clinical implementation has been hindered by, for example, B1 measurement accuracy, reconstruction artifacts resulting from inaccuracies in underlying models, and stringent hardware/software requirements. To address these challenges, we present a novel approach aimed at accurate and high-resolution EPs reconstruction based on water content maps by using a physics-informed network (PIN-wEPT). The proposed method utilizes standard clinical protocols and conventional multi-channel receive arrays that have been routinely equipped in clinical settings, thus eliminating the need for specialized RF sequence/coil configurations. Compared with the original wEPT method, the network generates accurate water content maps that effectively eliminate the influence of and by incorporating data mismatch with electrodynamic constraints derived from the Helmholtz equation. Subsequent regression analysis develops a broad relationship between water content and EPs across various types of brain tissue. A series of numerical simulations was conducted at 7 T to assess the feasibility and performance of the method, which encompassed four normal head models and models with tumorous tissues incorporated, and the results showed normalized mean square error below 1.0% in water content, below 11.7% in conductivity, and below 1.1% in permittivity reconstructions for normal brain tissues. Moreover, in vivo validations conducted over five healthy subjects at both 3 and 7 T showed reasonably good consistency with empirical EPs values across the white matter, gray matter, and cerebrospinal fluid. The PIN-wEPT method, with its demonstrated efficacy, flexibility, and compatibility with current MRI scanners, holds promising potential for future clinical application.

Robust Permittivity Reconstruction With the Transmission and Reflection Method at mm-Wave Frequencies

The permittivity reconstruction with the transmission and reflection method usually requires time-gating to mitigate distorted measurement data. State-of-the-art approaches reduce the available bandwidth as they introduce ringing. Available frequency extension approaches to avoid a bandwidth reduction are not based on a physically meaningful estimate. In this work, we propose a method that takes advantage of the information already given by the measurement to calculate a reasonable frequency extension. The inverse problem of the actual permittivity reconstruction is most commonly approached by the Baker-Jarvis algorithm from the National Institute of Standards and Technology (NIST) which considers the magnitude of one single complex number. It is calculated from the difference between measurement and model of the scattering matrix. In this article, we demonstrate the superiority of matching all four scattering parameters individually instead. This results in particular in a wider range of initial start parameters with proper convergence to the desired solution and more reliable reconstruction results for optimizations with unknown sample thickness. The benefits of the novel reconstruction techniques are demonstrated and evaluated in detail on simulation and measurement data in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V$</tex-math> </inline-formula> band.

Complex Permittivity Reconstruction Using Skin Surface Reflection and Neural Network for Microwave Breast Imaging

Complex Permittivity Reconstruction Using Skin Surface Reflection and Neural Network for Microwave Breast Imaging

Direct Permittivity Reconstruction From Power Measurements Using a Machine Learning Aided Method

A machine learning aided (MLA) method is employed for the direct permittivity retrieval of dispersive and non-dispersive materials. The method requires low-cost measurements since it solely utilizes the amplitude of the transmission response ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$|S_{21}|$</tex-math> </inline-formula> ) to extract the complex permittivity. This precludes the need for a network analyzer, and therefore, the measurements can be performed using a power sensor. Unlike earlier works, however, the method introduced here does not require prior information about the dispersion model of the material under test (MUT), so it is applicable to a wider range of materials. The method is based on applying two artificial neural networks (ANNs) for the permittivity reconstruction of low and high-loss materials. The ANNs are trained using full-wave simulation results of a coaxial line loaded with different MUTs for the direct reconstruction of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon^\prime$</tex-math> </inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon^{\prime\prime}$</tex-math> </inline-formula> . As a proof of concept, several chemical liquids, their mixtures, and powdered samples were used to experimentally validate the technique within the 0.3–3 GHz band. The retrieved complex permittivities of samples were in good agreement with the reference data and those obtained by the well-known transmission/reflection Nicolson–Ross–Weir (NRW) method.

Microwave Subsurface Imaging Method by Incorporating Radar and Tomographic Approaches

Due to its high resolution and deep penetration depth, microwave ultrawideband radar is a promising tool for the non-destructive testing (NDT) of transportation infrastructure. Microwave radiation can also be used to reconstruct the dielectric properties of objects and therefore can be used to detect an air cavity or metallic rust in concrete. We used contrast source inversion (CSI) as one of the most promising inverse scattering schemes. To resolve the observation domain limitations of NDT, radar imaging method, also known as range points migration (RPM) method, was first incorporated into the inverse scattering algorithm based on CSI as a region of interest (ROI) estimator, which substantially improves the accuracy of complex permittivity reconstruction. In addition, the ROI optimizing scheme based on the CSI cost function is used to enhance ROI accuracy. The effectiveness of the proposed methods is validated via finite-difference time-domain (FDTD)-based numerical simulation, which assumes typical NDT model.

Full-waveform inversion of ground-penetrating radar data in frequency-dependent media involving permittivity attenuation

SUMMARYFull-waveform inversion (FWI) of ground-penetrating radar (GPR) data has received particular attention in the past decade because it can provide high-resolution subsurface models of dielectric permittivity and electrical conductivity. In most GPR FWIs, these two parameters are regarded as frequency independent, which may lead to false estimates if they strongly depend on frequency, such as in shallow weathered zones. In this study, we develop frequency-dependent GPR FWI to solve this problem. Using the τ-method introduced in the research of viscoelastic waves, we define the permittivity attenuation parameter to quantify the attenuation resulting from the complex permittivity and to modify time-domain Maxwell’s equations. The new equations are self-adjoint so that we can use the same forward engine to back-propagate the adjoint sources and easily derive model gradients in GPR FWI. Frequency dependence analysis shows that permittivity attenuation acts as a low-pass filter, distorting the waveform and decaying the amplitude of the electromagnetic waves. The 2-D synthetic examples illustrate that permittivity attenuation has low sensitivity to the surface multioffset GPR data but is necessary for a good reconstruction of permittivity and conductivity models in frequency-dependent GPR FWI. As a comparison, frequency-independent GPR FWI produces more model artefacts and hardly reconstructs conductivity models dominated by permittivity attenuation. The 2-D field example shows that both FWIs reveal a triangle permittivity anomaly which proves to be a refilled trench. However, frequency-dependent GPR FWI provides a better fit to the observed data and a more robust conductivity reconstruction in a high permittivity attenuation environment. Our GPR FWI results are consistent with previous GPR and shallow-seismic measurements. This research greatly expands the application of GPR FWI in more complicated media.

Distorted Born iterative method with back-propagation improves permittivity reconstruction

AbstractThe distorted Born iterative method (DBIM) is a widely used quantitative reconstruction algorithm to solve the inverse scattering problems of microwave imaging. The major mathematical challenges in solving such problems are non-uniqueness, non-linearity, and ill-posedness. Due to these issues, the optimization algorithm converges to a local minimum. This drawback can be overcome by selecting the correct initial guess solution, which helps to escape local minima and thus guides the inversion algorithm to a satisfactory result. This study uses a back-propagation algorithm to calculate the initial estimate, which significantly accelerates the rate of convergence and improves the accuracy of the standard DBIM approach. The results of this method are compared with zero initialization and Born-approximated initialization. For comparison, weak as well as strong scattering profiles of synthetic and experimental dataset are considered. The results suggest that the proposed method provides a significant improvement in terms of computing cost and efficiency. Furthermore, the proposed technique has the potential to successfully push the limits of reconstructible contrast.

Fractional Regularized Distorted Born Iterative Method for Permittivity Reconstruction

Fractional Regularized Distorted Born Iterative Method for Permittivity Reconstruction

A Hybrid Algorithm Based on a Modified Sine Cosine Algorithm and Least Square and Its Application to Microwave Imaging

With the rapid development of materials science and medical imaging technology, traditional optimization algorithms cannot solve the problem of inverse scattering of complex scatterers well. Therefore, more and more imaging algorithms for solving complex scatterers were proposed. In this paper, a novel hybrid algorithm is put forward for the microwave imaging problem. First, the proposed algorithm improves the search path of the traditional sine cosine algorithm, which obtains better global search capability. Second, the least square is introduced to form judging and contrasting mechanisms, which forms the parallel algorithm simultaneously, in order to make the proposed algorithm more suitable for the diverse microwave imaging problem. To prove the efficiency of the proposed algorithm, several examples, including ten benchmark functions, two engineering design problems, and three different microwave imaging problem tests are adopted. As expected, the results show that the proposed algorithm achieves not only superior optimal value but also the reconstruction of the complicated permittivity of the scatterer compared with several traditional optimization algorithms.

Microwave Radiometric Coherence Imaging: A Novel Electromagnetic Imaging Technique

A new microwave (MW) imaging technique for the reconstruction of complex permittivity profiles of lossy dielectric objects is proposed. The proposed technique is based on partial coherence in thermal radiation of objects and is distinct from interferometric radiometry used for high-resolution imaging of brightness temperature. This is a unique feature of the method that distinguishes it from other MW imaging methods for permittivity reconstruction, where the underlying physical phenomenon is electromagnetic scattering by the probed object. Equations governing the imaging method are presented, and its potential for complex permittivity reconstruction in two dimensions is demonstrated with simulations.

Noise-Robust Microwave Breast Imaging Applied to Multi-Frequency Contrast Source Inversion

Ultra-wideband (UWB) microwave quantitative imaging offers less-painful examination, where a significant dielectric contrast between the malignant tumor and normal tissue is exploited. However, there are some difficulties in providing an accurate dielectric profile of breast media. This is because additive noises severely contaminate scattered signals. In this study, we apply a post-processing multi-frequency integration scheme to contrast source inversion (CSI) data to suppress image fluctuations. These are caused by the additive noise expected in a UWB system, which is also applicable to other inversion schemes. To deal with the dispersive dielectric properties in the CSI scheme, we introduce a first-derivative model of the Debye dispersion model to compensate for the dispersive effect. The FDTD numerical validations, using realistic breast phantoms with dispersive properties, show that a multi-frequency integration scheme considerably upgrades noise-robustness in complex permittivity reconstruction tissues.

Simultaneous Shape and Permittivity Reconstruction in ECT With Sparse Representation: Two-Phase Distribution Imaging

Electrical capacitance tomography (ECT) is a technique to visualize the permittivity distribution inside a domain from the interelectrode mutual capacitances on the domain boundary. The potential applications of ECT in nondestructive testing (NDT) depend on accurate and stable image reconstruction. To improve image quality, this article presents a reconstruction framework with the sparse representation of phase boundaries in two-phase distributions. By adopting a sparsity-promoting basis, i.e., radial basis functions, the reconstruction problem is transformed into searching for the optimal phase boundaries and real-permittivity values of inclusions by formulating an optimization problem accordingly. This can reduce the number of unknowns significantly and has a strong ability to accommodate to the topology changes of inclusion geometries, which can improve the reconstruction accuracy and robustness. Both simulation and phantom experiments are performed to investigate the reconstruction performance, especially regarding the antinoise ability and robustness against choices of model parameters. Compared with typical conventional methods, our method can not only provide significantly improved image quality but also accurately estimate the real-permittivity values of inclusions. This would enable ECT to be applied in challenging NDT applications.

Numerical Sensitivity Analysis for Dielectric Characterization of Biological Samples by Open-Ended Probe Technique.

Dielectric characterization of biological tissues has become a fundamental aspect of the design of medical treatments based on electromagnetic energy delivery and their pre-treatment planning. Among several measuring techniques proposed in the literature, broadband and minimally-invasive open-ended probe measurements are best-suited for biological tissues. However, several challenges related to measurement accuracy arise when dealing with biological tissues in both ex vivo and in vivo scenarios such as very constrained set-ups in terms of limited sample size and probe positioning. By means of the Finite Integration Technique in the CST Studio Suite® software, the numerical accuracy of the reconstruction of the complex permittivity of a high water-content tissue such as liver and a low water-content tissue such as fat is evaluated for different sample dimensions, different location of the probe, and considering the influence of the background environment. It is found that for high water-content tissues, the insertion depth of the probe into the sample is the most critical parameter on the accuracy of the reconstruction. Whereas when low water-content tissues are measured, the probe could be simply placed in contact with the surface of the sample but a deeper and wider sample is required to mitigate biasing effects from the background environment. The numerical analysis proves to be a valid tool to assess the suitability of a measurement set-up for a target accuracy threshold.

Regularized minimal residual method for permittivity reconstruction in microwave imaging

AbstractIn this paper, a regularized reconstruction based on the minimal residual method is proposed for microwave imaging applications. The method provides optimum regularization parameter to estimate the distribution of permittivity values of unknown scatterers under test. Initially, the method is applied to Born approximated linear model for weak scatterers. The performance of this approach is compared with the commonly adopted Morozov's discrepancy principle used in conjunction with the Tikhonov regularization. The effectiveness of the method is assisted by simulating the various numerical examples of synthetic and experimental data. The results of numerical simulations validate that the proposed method is highly effective. Thereafter, a non‐linear inverse problem based on the inexact Newton method is examined for the estimation of strong scatterers. Here also, the proposed method is found to be helpful in terms of improving the image accuracy.

Permittivity Reconstruction in Electrical Capacitance Tomography Based on Visual Representation of Deep Neural Network

Electrical Capacitance Tomography (ECT) has been developed for many years and made great progresses. Successful applications of ECT depend on the accuracy and speed of image reconstruction. In this paper, we propose a new image reconstruction method based on deep neural network. The proposed neural network mainly consists of three parts, i.e. a forward problem network, an inverse problem network and a permittivity prediction network. Compared to previous reconstruction algorithms, the benefit of our method is that it can not only reconstruct the object shape, but also predict its permittivity value with the preset resolution which is desired in many multiphase flow applications. In experiment, 10000 frames of simulation data and additional measured capacitance data were used. The results show that the proposed method can reconstruct images more accurately than typical iterative methods with real permittivity values of objects predicted correctly, and reduce the computational cost to about 2.24 seconds per frame for an image resolution of 200*200.

Permittivity Reconstruction of Nondispersive Materials Using Transmitted Power at Microwave Frequencies

This article presents a dielectric characterization method based on transmitted power measurements in the microwave regime for nondispersive materials. The method can retrieve the dielectric properties of materials utilizing multiobjective functions enforced at multiple frequencies without the need for phase information, which requires expensive measurement setups. Therefore, a signal generator and a power meter are all that is needed to retrieve the permittivity of materials. To validate the method numerically, two structures including free space and a coaxial line are used. For experimental verification, a coaxial line is designed and fabricated to retrieve the dielectric properties of several materials. Both simulation and measurement results show the high accuracy level of the proposed technique.

Magnetic resonance electrical property mapping at 21.1 T: a study of conductivity and permittivity in phantoms, ex vivo tissue and in vivo ischemia

Electrical properties (EP), namely conductivity and permittivity, can provide endogenous contrast for tissue characterization. Using electrical property tomography (EPT), maps of EP can be generated from conventional MRI data. This report investigates the feasibility and accuracy of EPT at 21.1 T for multiple RF coils and modes of operation using phantoms. Additionally, it demonstrates the EP of the in vivo rat brain with and without ischemia.Helmholtz-based EPT was implemented in its Full-form, which demands the complex field, and a simplified form requiring either just the field phase for conductivity or the field magnitude for permittivity. Experiments were conducted at 21.1 T using birdcage and saddle coils operated in linear or quadrature transceive mode, respectively. EPT approaches were evaluated using a phantom, ex and in vivo Sprague-Dawley rats under naïve conditions and ischemic stroke via transient middle cerebral artery occlusion.Different conductivity reconstruction approaches applied to the phantom displayed average errors of 12%–73% to the target acquired from dielectric probe measurements. Permittivity reconstructions showed higher agreement and an average 3%–8% error to the target depending on reconstruction approach. Conductivity and permittivity of ex and in vivo rodent brain were measured. Elevated EP in the ischemia region correlated with the increased sodium content and the influx of water intracellularly following ischemia in the lesion were detected.The Full-form technique generated from the linear birdcage provided the best accuracy for EP of the phantom. Phase-based conductivity and magnitude-based permittivity mapping provided reasonable estimates but also demonstrated the limitations of Helmholtz-based EPT at 21.1 T. Permittivity reconstruction was improved significantly over lower fields, suggesting a novel metric for in vivo brain studies. EPT applied to ischemic rat brain proved sensitivity to physiological changes, motivating the future application of more advanced reconstruction approaches.

Improved Tumor Detection via Quantitative Microwave Breast Imaging Using Eigenfunction-Based Prior

A multistage algorithm for quantitative microwave breast imaging is presented which utilizes the eigenfunction-based reconstruction of the complex-valued permittivity as prior information. The eigenfunction-based reconstruction is obtained from a single-frequency non-iterative microwave inversion technique that uses the eigenfunctions of the Helmholtz operator, in a resonant conductive enclosure, as the expansion basis. The low-resolution eigenfunction-based reconstruction is incorporated into the Contrast Source Inversion technique as an inhomogeneous numerical background. The use of this prior information improves the stability of the inversion algorithm, and results in better detectability of tumors. The multistage algorithm's performance is demonstrated by applying it to synthetic data obtained from three 2D MRI-derived anthropomorphic breast models with various densities, and shapes. The algorithm's efficacy in tumor detection is assessed by investigating detection results using prior information obtained with the number of eigenfunction in the expansion basis truncated with three different values. Numerical experiments are performed using four different frequencies. The main advantage of obtaining prior information using this method, as opposed e.g. in using radar or ultrasound derived prior, is that it utilizes the same microwave set-up, and only microwave interrogating fields.

Complex Permittivity Reconstruction for Microwave Imaging

本論文は，コンクリート非破壊検査等を想定したマイクロ波による複素誘電率イメージング法において，レーダとトモグラフィ法を融合させる方法を導入する．具体的には高精度レーダ画像化法であるRPM(Range Points Migration)法により関心領域(ROI(Region of Interest))を事前推定し，未知数を飛躍的に削減することでトモグラフィ法における推定精度の改善を図る．またCSI(Contrast Source Inversion)法におけるコスト関数を利用したROI更新アルゴリズムを導入し，レーダとトモグラフィの双方向の処理により，ROI及び複素誘電率推定精度の両方を改善することができることを数値計算例によって示す．