Contrast Source Research Articles

Deciphering centurial anthropogenic pollution processes in large lakes dominated by socio-economic impacts

Human activities have greatly increased the influx of pollutants into global freshwater ecosystems. Understanding the pollution patterns at multi-decadal scales, and how the socio-economic development and public policy have shaped them, are crucial to assess the current status of environmental quality and develop sound strategies for watershed management. This study takes the test case of large Taihu Lake (∼2,338 km2) in rapidly developing regions of China, to examine the temporal-spatial patterns and driving factors of centurial trace metal and metalloid contamination. Using comparative sedimentary records, we applied multiple geochemical indices and positive matrix factorization modelling to identify the anthropogenic versus natural sources and their contributions. Results identified cadmium, antimony and lead as typical pollutants, with high anthropogenic contribution rates of 58–79 %, 54–62 % and 28–36 %, respectively. Contamination histories were asynchronous across the lake, starting from the 1940s (North) to mid-1990s (East), following the gradient of socio-economic stressors of the sub-basins. Specifically, industrial and agricultural inputs through runoff and river networks were main sources of metal in the northern and western lake parts, accounting for ≥ 70 % since the 1980s. In contrast, aquaculture and agriculture related sources (≥ 80 %) dominated in Eastern Taihu Lake over the last decade. Moreover, atmospheric metal deposition from nearby industrial cities significantly affected the northern parts of the lake. The stationary and/or slightly decreased contamination trends, especially after 2000 AD, shed light into the effectiveness of recent environmental regulation. Our findings suggest, however, that agricultural non-point sources and legacy effects probably delayed reductions in the input of pollutants. Sustainable management of similar large watersheds worldwide, therefore, would benefit by highlighting the role of multiple anthropogenic sources, legacy contamination and lake-specific response.

Modeling of 3-D elastic waves in nonlinear elastic solids using the iterative nonlinear contrast source method

In nondestructive testing, the generation of higher harmonics and the mixing of elastic waves are used to measure the nonlinearity parameters, which in turn are closely related to the microscopic state of the material. A 3-D numerical tool that can simulate large scale, four-dimensional, nonlinear elastic wavefields would be very useful for the reliable interpretation of experimental results. Here, a method is presented that can efficiently compute the nonlinear displacement fields in a homogeneous, isotropic elastic medium, taking into account its third-order elastic constants (A, B, C). The method is based on the Neumann iterative solution of an integral equation involving a Green's function of the linear `background' medium, and a contrast source representing the nonlinearity of the medium. The integral equation is solved iteratively, and the computations are based on Fast Fourier Transforms using a sampling rate close to the Nyquist limit, i.e., two grid points of the shortest wavelength. The displacement fields are evaluated using the scalar and vector potential functions representing the compressional and shear displacements. In this presentation, the suitability of the INCS method for modeling the harmonics of 3-D nonlinear elastic waves and its validation by comparison with an analytical benchmark solution, will be presented.

Keeping the grid size under control: Nyquist sampling in the Iterative nonlinear contrast source method

Nonlinear propagation of ultrasound is applied in medical imaging and therapy, as well as in nondestructive testing. Development of dedicated equipment and protocols, and interpretation of results, is facilitated by reliable simulation of nonlinear ultrasound fields. Typical applications require accurate representation of higher harmonics with amplitudes 120 dB below the fundamental, over spatiotemporal domains that span several hundreds of wavelengths/periods of the fundamental. Finite-element and finite-difference schemes usually require 10–20 points per wavelength/period of the highest harmonic, without a way to restrict the number of harmonics involved in the solution. Solving the nonlinear wave equation with these methods may therefore require a prohibitively large computational grid. Alternatively, the nonlinear wave problem may be cast into an integral equation, which can be solved iteratively. This is the basis of our ever-expanding Iterative Nonlinear Contrast Source method. Most importantly, this approach allows to explicitly limit the wavenumber/frequency range included in the solution, and hence enables sampling at the Nyquist rate set by the highest desired frequency. As a consequence, the computational grid can be relatively small without introducing aliasing. This presentation elucidates how this is achieved by an appropriate combination of numerical filtering and windowing operations during each iteration.

Incremental distorted multiplicative regularized contrast source inversion for inhomogeneous background: The case of TM data

ABSTRACT The problem of electromagnetic inverse scattering under an inhomogeneous background is analyzed. This paper presents a modified contrast source inversion (CSI) method, named incremental distorted multiplicative regularized contrast source inversion (ID-MRCSI) to solve the inverse problems in two dimensions. By redefining data function, state function, and cost functional, the differences between the real target and the known arbitrary background can be reconstructed. Numerical results show that the ID-MRCSI algorithm is suitable for the applications of continuous repeated measurements to a specific target. It has the prospect of being utilized in the wearable imaging equipment to recover the information of changes dynamically.

Fourier Bases-Expansion Contraction Integral Equation for Inversion Highly Nonlinear Inverse Scattering Problem

The electromagnetic inverse scattering problems (ISPs) have counted severe multiple scattering effects, especially those for strong scatterers (the ones with high contrasts and/or electrically large dimensions). Iterative inversion methods based on the model of the Lippmann–Schwinger integral equation (LSIE) usually fail to reconstruct such highly nonlinear ISPs. In this article, in virtue of a new recently established contraction integral equation for inversion (CIE-I), we propose a Fourier bases-expansion with CIE-I (FBE-CIE-I) inversion method to handle highly nonlinear ISPs via the contrast source inversion (CSI) scheme. In the FBE-CIE-I, the unknown contrast source is spanned within the Fourier bases, and the multi-round optimization scheme is adopted by choosing the proper number of low-frequency components; not only the model of CIE-I can be stabilized well but also the computational cost can be further reduced compared with the traditional CSI. Besides, compared with the previous inversion method based on LSIE, the resolvability and robustness of the FBE-CIE-I could be significantly enhanced in handling highly nonlinear ISPs. Numerical and experimental tests verify the interests and efficiency of the proposed method.

Multi-parameter inversion with the aid of particle velocity field reconstruction

Multi-parameter inversion for medical ultrasound leads to an improved tissue classification. In general, simultaneous reconstruction of volume density of mass and compressibility would require knowledge of the particle velocity field along with the pressure field. However, in practice the particle velocity field is not measured. Here, the authors propose a method for multi-parameter inversion where the particle velocity field is reconstructed from the measured pressure field. To this end, the measured pressure field is described using outward propagating Hankel functions. For a synthetic setup, it is shown that the reconstructed particle velocity field matches the forward modelled particle velocity field. Next, the reconstructed particle velocity field is used together with the synthetically measured pressure field to reconstruct density and compressibility profiles with the aid of contrast source inversion. Finally, comparing the reconstructed speed of sound profiles obtained via single-parameter versus multi-parameter inversion shows that multi-parameter outperforms single-parameter inversion with respect to accuracy and stability.

Alternating direction method of multiplier for solving electromagnetic inverse scattering problems

AbstractIn this paper, a novel alternating direction method of multiplier (ADMM) is proposed to solve the inverse scattering problems. The proposed method is suitable for a wide range of applications with electromagnetic detection. In order to solve the internal ill-posed problem of the integral equation and make the reconstructed images more closer to the ground truth, first, the augmented Lagrangian method is introduced to transform the complex constrained optimization problem into the extremum problem of unconstrained cost function. Therefore, two artificial regularization factors of the cost function are optimized. Then, this proposed method decomposes the unconstrained global problem in the inversion process into three linear sub-problem forms of contrast source function, contrast function, and dual variables. And the form of the updated algebra for each sub-problem is not complicated. By cross-iterating and updating contrast source function, contrast function, and dual variables, the global minimization of the cost function can be accurately found. Finally, the proposed method is compared with the existing well-known iterative method for solving the inverse scattering problem. Both the numerical and experimental tests verify the validity and accuracy of the proposed ADMM.

A multi-focusing contrast source Bayesian compressive method for solving inverse scattering problems

This work presents a novel inverse scattering (IS) methodology to deal wit.li the retrieval of the electromagnetic (EM) properties of unknown scat.t.erers. The proposed technique is based on the effective combination of a customized Bayesian compressive sensing (BCS) solver wit.li the iterative multi-scaling approach (IMSA). Accordingly, a-priori information on the class of imaged targets as well as progressively acquired information on their location and size is exploited to yield accurate and robust reconstructions. Moreover, a contrast source inversion (CSI) formulation is adopted in order to enable the retrieval of lion-Born scat.t.erers. Numerical results are shown to verify the effectiveness of the proposed IMSA-BCS-CSI method, as well as to compare it with state-of-the-art alternatives.

NDT/NDE by means of a probabilistic differential compressive sensing method

A novel microwave imaging (MI) method is proposed to deal with the nondestructive testing and evaluation (NDT/NDE) of dielectric structures. The proposed technique exploits a probabilistic differential contrast source inversion (D-CSI) formulation of the inverse scattering (IS) problem, which is then effectively solved by means of a customized multi-task Bayesian compressive sensing (MT-BCS) solver. Numerical results are shown to assess the effectiveness and robustness of the proposed NDT/NDE method, as well as to compare it. with a single-task (ST-BCS) implementation within the same framework.

Study on 3-D Acoustic Imaging for Human Thorax Based on Contrast Source Inversion.

In this article, we study a 3-D acoustic imaging algorithm that can reconstruct compressibility, attenuation, and density simultaneously based on the contrast source inversion (CSI) method. This is a nonlinear and ill-posed inverse problem. To deal with the nonlinearity, we introduce two asymmetrical contrast sources that are functions of the contrasts and the total field. In this case, the scattered field and the total field are linear with the two contrast sources, and the two contrast sources are also linear with the two contrasts; thus, the nonlinearity is partially alleviated. To mitigate the ill-posedness of this inverse problem, we apply a multifrequency, multitransmitter, and multireceiver setting. Besides, to ensure the robustness of the algorithm, two multiplicative regularization terms are introduced as additional constraints. The reconstruction of those acoustic parameters can be achieved by alternately updating the contrast sources and the contrasts from the knowledge of the pressure field. Numerical studies show good reconstruction of compressibility, attenuation, and density of the synthetic thorax model, which validates the feasibility of imaging human thorax using low-frequency ultrasound.

Phaseless Microwave Tomography Assessment for Breast Imaging: Preliminary Results

In the present work, a phaseless approach for microwave imaging applications is presented. The proposed solution strategy is based on the formulation of the scattering phenomena in terms of contrast source, while no phase-recovery stage is involved into the numerical procedure, thus providing a phaseless single-step resolution method. The image recovering potentialities of the discussed method are numerically validated by successfully distinguishing different tissues of a slice breast model, with a tumor located wherein. The above preliminary assessment encourages the adoption of the proposed solution in the framework of biomedical imaging.

Subwavelength Microstructure Probing by Binary- Specialized Methods: Contrast Source and Convolutional Neural Networks

Time-harmonic transverse-magnetic electromagnetic probing of a grid-like, finite set of infinitely long circular cylindrical dielectric rods affected by missing ones is investigated. Subwavelength distances between adjacent rods and subwavelength rod diameters are assumed, and this leads to a severe challenge due to the need of superresolution within the present microstructure, well beyond the Rayleigh criterion. A binary case is focused on: all rods have the same permittivity, but an unknown number of them are missing, the aim being to detect those within the resulting damaged microstructure from far-field data. Two binary-specialized methods are developed to that effect. One builds upon the iterative contrast-source inversion (CSI) with enforcing a binary contrast inside it. The other is set within a machine learning framework and uses convolutional neural networks (CNNs). The CSI version is mostly used as a reference for the CNN one. Comprehensive numerical simulations in configurations of interest in terms of organization of the microstructure, missing rods, frequency of observation, data acquisition, and noise are proposed. The binary-specialized CNN method appears powerful, upon proper training as expected, and outperforms the binary-specialized CSI method in terms of computational burden, quality of the probing, and versatility.

Accurate and robust inversion of buried objects based on the linear sampling method and differential evolution

The authors propose an accurate and robust method to reconstruct buried objects for half-space scenarios. First, the linear sampling method (LSM) was employed to estimate targets support. A relaxed threshold is defined for LSM to ensure all real targets are included. Despite the low accuracy of the estimation by LSM, the authors were more interested in its insensitivity to noise. Second, differential evolution (DE) optimisation was used to refine the LSM results. Since the magnitudes of LSM indicator functions are related to the probability of support belonging to real targets, different weights for gene elements are allocated according to their indicator values to control mutation and cross probability. A mask-beneficial contrast source inversion (CSI) is employed to evaluate cost function by encoding possible targets support and making it into a support mask. The mask is combined with CSI as a priori information and an accurate mask tends to derive a slight iteration error, whereas those incorrect ones will result in large errors. Thus, by adopting CSI iteration error as a cost function and taking advantage of superior optimisation performance of weighted DE, the authors find an optimum mask and reconstruct contrast with high fidelity. Effectiveness of the proposed method is validated by simulation results.

Truncated singular value decomposition for through‐the‐wall microwave imaging application

We considered differential through-the-wall microwave imaging with different formulations of truncated singular value decomposition (TSVD) method with a non-anechoic experiment. Previous studies employ TSVD with single transmitting/measuring antenna, while we show how to apply the TSVD in case of a moving linear transmitting/measuring antenna array. Particularly, an averaging scheme is employed for repeated measurements. Three TSVD approaches are tested: (i) TSVD on Contrast Source, (ii) TSVD on Contrast, (iii) multi frequency TSVD on Contrast. For (i), the dimension of inverted matrix is relatively low. After solving equations, a normalisation is proposed for eliminating noise. For (ii), the reconstructions get better compared to (i) since measured data for all excitations are inverted simultaneously. Nevertheless, (ii) requires more time than (i), since the inverted matrix gets larger. Finally, for (iii), to avoid additional calibration, we employ the solutions of (ii). Then, the contrasts are estimated for all frequencies and excitations simultaneously. Thus, the inverted matrix is largest for (iii), accuracy is best, computational time is longest. For testing proposed techniques, a metallic scatterer is deployed behind a wall. Results show trade-off between accuracy and computational time for choosing the suitable inversion method. Moreover, norm type selection is assessed for each method.

Three-Dimensional Joint Inversion of EM and Acoustic Data Based on Contrast Source Inversion

In this article, we study a 3-D joint inversion algorithm for acoustic and electromagnetic data. This algorithm is based on the contrast source inversion method, which aims to reconstruct acoustic and electromagnetic parameters by updating two contrasts and two contrast sources alternately. The contrast is defined as the relative difference between the parameter, such as permittivity, of the object and the background, while the contrast source is expressed as the function of the contrast and the total field to partially linearize the problem. Besides, two multiplicative regularization terms are employed to alleviate the ill-posedness. Because the physical parameters in electromagnetics and acoustics share the same structure, we use the gradient of the contrast in acoustics and electromagnetics to constrain each other to achieve the enhanced structural similarity between inverted models. Then, by minimizing the predefined cost function using the conjugate gradient method, those acoustic and electromagnetic parameters, such as compressibility, attenuation, permittivity, and conductivity, can be reconstructed. Two numerical examples are given to compare the results of separate inversion and joint inversion.

Solving Phaseless Highly Nonlinear Inverse Scattering Problems With Contraction Integral Equation for Inversion

At high frequencies, phase measurement is difficult to meet the accuracy required for imaging, and it is more susceptible to noise pollution. Consequently, it is important to develop inversion models and algorithms for electromagnetic inverse scattering problems with phaseless data (PD-ISPs). Compared to the ISPs with full-data (FD-ISPs), the PD-ISPs are more nonlinear due to the lack of the phase information. Aiming at solving highly nonlinear PD-ISPs, in this article we present a contraction integral equation for inversion (CIE-I) regularized with Fourier subspace via contrast source inversion method, denoted as PD-CSI-CIE-I. Under the model of CIE-I, the nonlinearity of PD-ISPs can be effectively alleviated. In order to stabilize CIE-I, a nested optimization scheme with multi-round procedure is adopted by choosing the proper number of low-frequency components from unknown induced current spanned in the Fourier subspace. By the Fourier bases expansion of induced current, the computational cost can be further reduced. Numerical and experimental examples validate the efficiency of the proposed inversion method. Futher, it is shown that the proposed PD-CSI-CIE-I has a stronger inversion capability than the one with the Lippmann-Schwinger integral equation (LSIE) when tackling high contrast scatterers with phaseless data.

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.

A Fast Inverse Scattering Imaging Method by Applying Virtual Experiments to T-Matrix Scheme

As a non-iterative linear inverse scattering imaging method, the linear sampling method (LSM) has the merits of easy implementation and high computational efficiency. In this article, based on the LSM and T-matrix method, we propose a fast method to reconstruct the target medium parameters. First, we use the LSM qualitative imaging method to estimate the contour of the target. Then, the preprocessing information of the LSM is applied to the virtual experiment circles in the framework of T-matrix method. In this way, we avoid the inversion of the matrix and only need to solve a series of univariate equations. Numerical simulation results show that the reconstruction accuracy of the proposed method is similar to that of LSM quantitative imaging method, but it has higher calculation accuracy and wider application range. Although the calculation accuracy is not as good as the contrast source inversion (CSI) method, the proposed method has huge advantages in terms of calculation efficiency.

Microwave Breast Imaging With Prior Ultrasound Information

Aiming at early detection of tumors, microwave breast imaging is investigated with \textit{a priori} information on tissue boundaries yielded from ultrasound reflection data. A regularization term is to incorporate the information that two neighboring pixels should exhibit similar dielectric properties when not on a boundary while a jump would be allowed otherwise. This regularization is enforced in the distorted Born iterative method and in the contrast source inversion method. Comprehensive numerical experiments are carried out, involving a simple synthetic model and on two anatomically-realistic MRI-derived numerical breast phantoms. Imaging quality appears greatly improved with this regularization when tissue boundaries are indeed provided. Improvement is observed also when real parts and imaginary parts are retrieved in separate fashion

Combining deep learning and 3D contrast source inversion in MR-based electrical properties tomography.

Magnetic resonance electrical properties tomography (MR‐EPT) is a technique used to estimate the conductivity and permittivity of tissues from MR measurements of the transmit magnetic field. Different reconstruction methods are available; however, all these methods present several limitations, which hamper the clinical applicability. Standard Helmholtz‐based MR‐EPT methods are severely affected by noise. Iterative reconstruction methods such as contrast source inversion electrical properties tomography (CSI‐EPT) are typically time‐consuming and are dependent on their initialization. Deep learning (DL) based methods require a large amount of training data before sufficient generalization can be achieved. Here, we investigate the benefits achievable using a hybrid approach, that is, using MR‐EPT or DL‐EPT as initialization guesses for standard 3D CSI‐EPT. Using realistic electromagnetic simulations at 3 and 7 T, the accuracy and precision of hybrid CSI reconstructions are compared with those of standard 3D CSI‐EPT reconstructions. Our results indicate that a hybrid method consisting of an initial DL‐EPT reconstruction followed by a 3D CSI‐EPT reconstruction would be beneficial. DL‐EPT combined with standard 3D CSI‐EPT exploits the power of data‐driven DL‐based EPT reconstructions, while the subsequent CSI‐EPT facilitates a better generalization by providing data consistency.