Contrast Source Inversion Algorithm Research Articles

Towards Intelligent Electromagnetic Inverse Scattering Using Deep Learning Techniques and Information Metasurfaces

Electromagnetic inverse scattering (EMIS) is uniquely positioned among many inversion methods because it enables to image the scene in a contactless, quantitative and super-resolution way. Although many EMIS approaches have been proposed to date, they usually suffer from two important challenges, i.e., time-consuming data acquisition and computationally -prohibitive data post processing, especially for large-scale objects with high and even moderate contrasts. To tackle the challenges, we here propose a framework of intelligent EMIS with the aid of deep learning techniques and information metasurfaces, enabling to the efficient data acquisition and instant data processing in a smart way. Towards this goal, as illustrative examples, we considerably extend the canonical contrast source inversion (CSI) algorithm, a canonical EMIS method by updating the contrast via the generative adversarial network (GAN), an unsupervised deep learning approach, leading to a novel physics-informed unsupervised deep learning method for EMIS, referred to as CSI-GAN in short. Compared with existing deep learning solutions for EMIS, our method relies on the supervision of physical law instead of the labeled training dataset, beating the bottleneck arising from the collection of labeled training datasets. Furthermore, we propose a scheme of adaptive data acquisition with the use of information metasurface in a cost-efficiency way, remarkably reducing the number of measurements and thus speeding up the data acquisition but maintaining the reconstruction's quality. Illustrative examples are provided to demonstrate the performance gain in terms of reconstruction quality, showing the promising potentials for providing the intelligent scheme for the EMIS problems.

Deep Learning Enhanced Contrast Source Inversion for Microwave Breast Cancer Imaging Modality

This study presents a deep-learning (DL) based contrast source inversion (CSI) algorithm for quantitative microwave breast cancer imaging. Inverse scattering analysis for quantitative dielectric profile reconstruction is promising for a higher recognition rate for cancer detection, especially for malignant breast tumors. We focus on CSI as a low complexity approach, and implement a deep convolutional autoencorder (CAE) scheme using radar raw-data, which enhances the convergence speed and reconstruction accuracy. Numerical tests using MRI-derived realistic phantoms demonstrate that the proposed method significantly enhances the reconstruction performance of the CSI.

Monitoring Bone Density Using Microwave Tomography of Human Legs: A Numerical Feasibility Study.

A major cause of bone mass loss worldwide is osteoporosis. X-ray is considered to be the gold-standard technique to diagnose this disease. However, there is currently a need for an alternative modality due to the ionizing radiations used in X-rays. In this vein, we conducted a numerical study herein to investigate the feasibility of using microwave tomography (MWT) to detect bone density variations that are correlated to variations in the complex relative permittivity within the reconstructed images. This study was performed using an in-house finite-element method contrast source inversion algorithm (FEM-CSI). Three anatomically-realistic human leg models based on magnetic resonance imaging reconstructions were created. Each model represents a leg with a distinct fat layer thickness; thus, the three models are for legs with thin, medium, and thick fat layers. In addition to using conventional matching media in the numerical study, the use of commercially available and cheap ultrasound gel was evaluated prior to bone image analysis. The inversion algorithm successfully localized bones in the thin and medium fat scenarios. In addition, bone volume variations were found to be inversely proportional to their relative permittivity in the reconstructed images with the root mean square error as low as 2.54. The observations found in this study suggest MWT as a promising bone imaging modality owing to its safe and non-ionizing radiations used in imaging objects with high quality.

Superlens Enhanced 2-D Microwave Tomography With Contrast Source Inversion Method

The contrast source inversion (CSI) algorithm is one of the primary techniques used for solution of non-linear inverse problems in microwave tomography. In this paper, we describe a modification of the CSI method adapted to imaging of the 2-D objects in the presence of the focusing media under TM-polarization. The focusing media is presented in the form of the Veselago lens. The data domain and imaging domain are properly positioned with respect to the location of the lens. Specifically, the sensors are located at the focal points of the lens with respect to the location of the individual pixels discretizing the contrast source. Such positioning of the source and observation locations in the presence of the lens, eliminates rank deficiency in the formulation of the inverse problem and results in significant improvements to both convergence speed of underlying conjugate gradient iterations and the accuracy of the image reconstruction in the CSI method.

Improvement of Multi-Frequency Microwave Breast Imaging through Frequency Cycling and Tissue-Dependent Mapping

Two modifications of the Contrast Source Inversion (CSI) algorithm have been employed to improve resulting 2-D microwave images of the dielectric properties of synthetic breast models produced using a well-established frequency-hopping technique. First, while reconstructions from low-frequency data are often used as initial guesses for otherwise unstable higher-frequency inversions, an improvement in overall image quality can be observed when the imaginary part of the reconstructed low-frequency image is altered to reflect the identical tissue geometry as its real part when used as an initial guess during subsequent reconstructions. Second, in such frequency-hopping scenarios, rather than terminating reconstructions following inversions of the highest frequency data, “frequency cycling” (i.e., returning to the lowest frequency in the sequence) can be used to further improve reconstructions without loss of resolution or anatomical detail.

Novel Stopping Criteria for Optimization-Based Microwave Breast Imaging Algorithms.

A discontinuous Galerkin formulation of the Contrast Source Inversion algorithm (DGM-CSI) for microwave breast imaging employing a frequency-cycling reconstruction technique has been modified here to include a set of automated stopping criteria that determine a suitable time to shift imaging frequencies and to globally terminate the reconstruction. Recent studies have explored the use of tissue-dependent geometrical mapping of the well-reconstructed real part to its imaginary part as initial guesses during consecutive frequency hops. This practice was shown to improve resulting 2D images of the dielectric properties of synthetic breast models, but a fixed number of iterations was used to halt DGM-CSI inversions arbitrarily. Herein, a new set of stopping conditions is introduced based on an intelligent statistical analysis of a window of past iterations of data error using the two-sample Kolmogorov-Smirnov (K-S) test. This non-parametric goodness-of-fit test establishes a pattern in the data error distribution, indicating an appropriate time to shift frequencies, or terminate the algorithm. The proposed stopping criteria are shown to improve the efficiency of DGM-CSI while yielding images of equivalent quality to assigning an often liberally overestimated number of iterations per reconstruction.

Hybridizable Discontinuous Galerkin Method Contrast Source Inversion of 2-D and 3-D Dielectric and Magnetic Targets

We present a microwave imaging algorithm capable of simultaneously reconstructing electric and magnetic targets from both electric and magnetic field measurement data, with support for arbitrary imaging system boundaries and inhomogeneous background media. A high-order time-harmonic discontinuous Galerkin method (DGM) forward solver is adopted within a contrast source inversion (CSI) algorithm formulated for electric and magnetic targets. Due to its high-order capabilities, the DGM forward solver effectively decouples the contrast and field discretizations without introducing a dual mesh. The drawback of standard DGM forward solvers, namely, their high computational cost, is addressed by a hybridizable DGM (HDGM) formulation. Synthetic and experimental results for both DGM-CSI and HDGM-CSI are presented for a variety of 2-D and 3-D measurement configurations and both dielectric and magnetic targets. HDGM-CSI is shown to have imaging performance comparable to FEM-CSI for dielectric targets, and significant additional flexibility that will enable future electromagnetic imaging applications and system design.

Study on Joint Inversion Algorithm of Acoustic and Electromagnetic Data in Biomedical Imaging

In this paper, we study a joint inversion algorithm to reconstruct acoustic and electromagnetic (EM) data in biomedical imaging. This algorithm is based on contrast source inversion algorithm. We define contrast source and contrast functions in both acoustics and EMs, respectively, and apply two reciprocal regularization operators to link acoustic and EM inversion. By minimizing the cost function using the conjugate gradient method, we can simultaneously reconstruct compressibility, attenuation, permittivity, and conductivity of different human tissues. Numerical experiments show that acoustic and EM inversion can compensate each other and achieve a better reconstruction than individual inversion. Besides, the joint inversion method is particularly sensitive to compressibility and conductivity and thus may be used to monitor air and water contents in human thorax as well as other applications in biomedicine.

Use of Field-Perturbing Elements to Increase Nonredundant Data for Microwave Imaging Systems

Field-perturbing elements (FPEs) are introduced for microwave imaging. These elements affect the imaging performance by increasing the amount of nonredundant data. Although this technique can be implemented in nonmetallic chambers, it is especially effective inside metallic enclosures where small perturbations can change the interrogating fields significantly. Results of simulations and a numerical investigation based on synthetic data are presented. The method is validated using an experimental system comprised of 24 coresident radially oriented monopoles that collect the normal component of the electric field on the inside surface of the enclosure. The measured data are used as input to a finite-element contrast source inversion algorithm. To investigate the effectiveness of the approach, a second experimental example is presented where a simplistic breast phantom with a tumor inclusion is imaged inside a smaller cylindrical chamber with 18 radially oriented monopoles and a single FPE. Because FPEs are easy to manufacture and are low costs, they can reduce the cost of an imaging system significantly by reducing the number of required RF ports, as well as reducing the system complexity and modeling error.

Microwave Imaging Using Normal Electric-Field Components Inside Metallic Resonant Chambers

A novel 3-D microwave imaging approach performed within a resonant air-filled metallic chamber is introduced and investigated. The new method utilizes the measurements of normal electric-field components at discrete points along the metallic chamber’s wall—near the chamber-wall boundary, the normal-field components are dominant, while the tangential components vanish. The inversion algorithm fully incorporates the resonant features of the low-loss chamber. A numerical study is used to quantify the imaging performance of using this technique compared with the traditional unbounded domain imaging. An experimental system is presented where the electric field is collected using 24 antennas distributed in three circumferential layers around an object of interest located inside the circular-cylindrical metallic chamber. For collecting the normal component of the field, two types of linearly polarized antennas are investigated: $\lambda /4$ monopole antennas and specially designed reconfigurable antennas (RAs), both projecting perpendicularly out from the chamber walls into the enclosure. The measured data are calibrated and then inverted using a multiplicatively regularized finite-element contrast source inversion algorithm. Using 3-D reconstructions of simple dielectric targets, it is shown that utilizing the RAs improves imaging performance due to a reduction in the modeling error introduced in the inversion algorithm.

Acceleration of 2-D Multiplicative Regularized Contrast Source Inversion Algorithm Using Paralleled Computing Architecture

Nonlinear inversion algorithms of electromagnetic data have been widely used. However, computational cost is still one of the bottlenecks for their applications. In this letter, we study an acceleration scheme for the multifrequency multiplicative regularized contrast source inversion algorithm using compute unified device architecture and graphic process unit (GPU). Numerical results show that the optimized algorithm on paralleled computing device outperforms the one on CPU processors with a significant reduction on computing time while keeping the same level of reconstruction quality. By using this algorithm, we successfully invert the microwave experimental data (2-D Fresnel dataset) in only a few minutes.

Surface-Current Measurements as Data for Electromagnetic Imaging Within Metallic Enclosures

A 3-D microwave imaging method within metallic enclosures is investigated and improved. This method uses the components of the surface-current vector at receiver points on the enclosure wall as data. At the metallic wall, the normal component of the magnetic field as well as the tangential components of the electric field is negligible, whereas the vectorial surface current, which is directly related to the tangential components of the magnetic field, is dominant. After presenting the results of a numerical investigation based on synthetic data, the method is validated using an experimental system comprised of 24 co-resident shielded, coaxial half-loop antennas, distributed in four layers, within a cylindrical metallic enclosure. These antennas are used in receiver–transmitter pairs to introduce an electromagnetic field into the chamber and collect the magnetic field at the receiver points. The measured data are used as input to a multiplicatively regularized finite-element contrast source inversion algorithm. Due to their relatively small size and minimal protrusion into the chamber, these antennas minimally perturb the field distribution inside the chamber and thereby allow the use of a simple numerical inversion model, which does not need to account for the passive antennas. These attributes are especially useful for large computationally intensive industrial applications. The experimental system described herein is a laboratory-scale prototype for a stored-grain imaging application where metallic silos are utilized.

Grain bin monitoring via electromagnetic imaging

Stored grain monitoring is an important post-harvest stage of the food production chain. Grains are usually stored in large metal containers referred to as bins or silos. During storage, there is a possibility for grain to spoil and become unusable. Therefore, monitoring of grain bins is essential to detect conditions leading to spoilage within the bin. Most current grain bin monitoring techniques lack sensitivity as they require conditions leading to spoilage to surpass a certain limit before detection is possible, and consequently a large amount of stored grain is lost during monitored storage. This paper presents the advances in developing a novel grain-monitoring technique using electromagnetic imaging, a modality that can provide global, quantitative images of grain properties throughout the bin. Side-mounted antennas illuminate the contents of the bin and a set of receivers measures the electromagnetic energy within the bin at discrete locations. Using these measurements an optimization algorithm attempts to reconstruct the contents of the bin – herein a finite-element contrast source inversion (FEM-CSI) algorithm was used. The result is a global map of the electrical properties of the grain throughout the bin. In this work we first present a synthetic validation of the proposed method for a model of a full scale hopper bin using simulations to produce the electromagnetic field data. Next, a scaled experimental system was used to collect data from grain that contained regions of induced contamination. This data was used to produce images that show the applicability of the method in practice. Results suggest that this technology has potential to provide farmers with a reliable and robust method to remotely monitor stored grain, preserving stored food resources and increasing their revenue.

Regularized seismic velocity inversion based on inverse scattering theory

In this paper, the regularized finite difference contrast source inversion algorithm based on inverse scattering theory is utilized to invert the seismic velocity distribution in the underground medium, and this algorithm is a waveform inversion method in frequency domain based on wave equation. Velocity distribution is updated iteratively by minimizing the cost function using the nonlinear conjugate gradient method. The geophysical inversion problem has the characters of ill-posedness and instability, we handle this problem by adding an additional regularization item based on total variation of inversion parameter, making the inversion problem become a well-posed problem, and the algorithm has the ability of anti-noise interference. In the inversion process we use the frequency-space domain 9-point difference propagation operator under PML absorption boundary condition. Compared with other inversion algorithm, the construction of forward modeling operator and other matrix factorization calculation process can be avoided in each iterative step because the background medium remains unchanged throughout the inversion process, this makes the algorithm more suitable for large-scale three-dimensional inversion. In addition, the MPI parallel computation is applied, by which the efficiency of inversion process is improved greatly. The two-dimensional CSEG model inversion results show that this algorithm can obtain high resolution seismic velocity reconstruction, and provide an accurate velocity information for seismic data processing and interpretation.

A 3-D Dual-Polarized Near-Field Microwave Imaging System

A novel 3-D dual-polarized microwave imaging system based on the modulated scattering technique (MST) is presented. The system collects the magnitude and phase of the scattered field using 120 MST probes and 12 transmitter/collector antennas distributed around an object-of-interest in the near-field region. The 12 antennas form a middle circumferential layer while the printed MST probes are arranged on three circumferential layers including the middle layer. The antennas are linearly polarized double-layer Vivaldi antennas, each fixed inside its own cylindrical conducting cavity and slanted with respect to the vertical axis of the imaging chamber. The MST probes are etched on both sides of a thin substrate and loaded with five evenly distributed p-i-n diodes along their length. These are positioned vertically and horizontally so that the z- and φ-components of the electric field is measured. Field data are collected using MST, calibrated, and then inverted using a multiplicatively regularized finite-element contrast source inversion algorithm. The system performance is evaluated by collecting and inverting data from different 3-D targets.

Application of contrast source inversion algorithm to image restruction of 2-D hybrid targets

In view of the limited accuracy of imaging algorithm,the nonlinear Contrast Source Inversion(CSI) algorithm combined with regularization and Concurrent Frequency(CF) was proposed for reconstructing a hybrid target in an anechoic chamber.The experimental data were obtained using multi-frequency multi-bistatic measurements.The reconstructed position,shape and contrast value of the target were presented,verifying the accuracy of the extended CSI algorithm for reconstructing the complicated 2-D hybrid targets.

Contrast Source Inversion Algorithm Against Three Dimensional Microwave Experimental Data

This paper describes a nonlinear inversion scheme for reconstructing two three-dimensional (3-D) homogeneous dielectric targets in an anechoic chamber in a controlled environment. The applied scheme is the contrast source inversion (CSI) algorithm, a nonlinear iterative algorithm based on two domain integral equations, combined with frequency hopping (FH) approach. The inversion results, which are presented and compared for the 3-D co-polarized data, verify the capability and the accuracy of the CSI algorithm with CF approach for 3-D microwave imaging.

A contrast source inversion method in the wavelet domain

We present a contrast source inversion (CSI) algorithm using truncated wavelet representations. Specifically, we represent the unknown contrast sources and the contrast function in terms of the wavelet basis functions. In order to reduce the number of wavelet coefficients for these unknowns, we apply a progressive multiscale truncation scheme based on the reconstructed contrast function. This approach increases the robustness of the CSI algorithm for noisy or limited data, and decreases the computation time as well as the memory usage. We tested the wavelet-domain CSI method using both synthetic and experimental data. The numerical experiments show that similar results with the regular spatial-domain CSI method are obtained when the number of (independent) measurement data points is comparable to the number of the unknowns in the contrast function. The advantages of the wavelet-domain CSI method become apparent as we deal with cases where the number of measurement data points is smaller than the number of unknowns in the contrast function.

A study of matching fluid loss in a biomedical microwave tomography system

Effective imaging of human tissue with microwave tomography systems requires a matching fluid to reduce the wave reflections at the tissue boundary. Further, in order to match the idealized mathematical model used for imaging with the complicated physical measurement environment, loss must be added to the matching fluid. Both too little and too much loss result in low-quality images, but due to the nonlinear nature of the imaging problem, the exact nature of loss-to-image quality cannot be predicted a priori. Possible optimal loss levels include a single, highly sensitive value, or a broad range of acceptable losses. Herein, the authors outline a process of determining an appropriate level of loss inside the matching fluid and attempt to determine the bounds for which the images are the highest quality. Our biomedical microwave tomography system is designed for 2D limb imaging, operating from 0.8 to 1.2 GHz. Our matching fluid consists of deionized water with various levels of loss introduced by the addition of table salt. Using two homogeneous tissue-mimicking phantoms, and eight different matching fluids of varying salt concentrations, the authors introduce quantitative image quality metrics based on L-norms, mean values, and standard deviations to test the tomography system and assess image quality. Images are generated with a balanced multiplicative regularized contrast source inversion algorithm. The authors further generate images of a human forearm which may be analyzed qualitatively. The image metrics for the phantoms support the claim that the worst images occur at the extremes of high and low salt concentrations. Importantly, the image metrics show that there exists a broad range of salt concentrations that result in high-quality images, not a single optimal value. In particular, 2.5-4.5 g of table salt per liter of deionized water provide the best reconstruction quality for simple phantoms. The authors argue that qualitatively, the human forearm data provide the best images at approximately the same salt concentrations. There exists a relatively large-range of matching fluid losses (i.e., salt concentrations) that provide similar image quality. In particular, it is not necessary to spend time highly optimizing the level of loss in the matching fluid.

FULL-VECTORIAL PARALLEL FINITE-ELEMENT CONTRAST SOURCE INVERSION METHOD

The multiplicatively regularized flnite-element contrast source inversion algorithm (MR-FEM-CSI) is used to solve the full- vectorial three-dimensional (3D) inverse scattering problem. The contrast and contrast-source optimization variables are located at the centroids of tetrahedra within the problem domain; whereas the electric fleld is expanded in terms of edge basis functions on the same tetrahedra. A dual-mesh is created in order to apply the multiplicative regularization. To handle large-scale problems the inversion algorithm is parallelized using the MPI library, with sparse matrix and vector computations supported by PETSc. The algorithm is tested using experimental datasets obtained from the Institut Fresnel database. A synthetic example shows that the technique is able to successfully image moisture hot-spots within a partially fllled grain bin.