Multiplicative Regularized Contrast Source Inversion Research Articles

The Incident Field Optimization Method for the Electromagnetic Inverse Problems

In this letter, an incident field optimization (IO) method integrated with contrast source inversion (CSI) method and multiplicative regularized CSI (MR-CSI) method is proposed to deal with the electromagnetic inverse problems. For the conventional iterative inversion methods, the incident field is a prior knowledge and is usually obtained by the calibration process. Through the synthetic data experiments, it can be found that a small distortion of the incident field has little impact on the inversion results, but a high distortion will lead to fault inversion results or no convergence. In this letter, the incident field optimal factor, being updated during the iterative process, is introduced into the CSI and MR-CSI method, named as IO-CSI and MR–IO–CSI. The new methods have good inversion performance even with high incident field distortion. The proposed methods are applied to the Fresnel experiment data directly without the calibration procedure. Both the single-frequency and multifrequency inversion experiments demonstrate that the IO-CSI and MR–IO–CSI method can achieve good inversion results, indicating the method’s practical applicability.

Adaptive Clustering Distorted Born Iterative Method for Microwave Brain Tomography With Stroke Detection and Classification.

A modified distorted Born iterative method (DBIM), which includes clustering of reconstructed electrical properties (EPs) after certain iterations, is presented for brain imaging aiming at stroke detection and classification. For this approach to work, a rough estimation of number of different materials (or bio-tissues) in the imaged domain and their corresponding rough dielectric properties (permittivity and conductivity) are needed as a prior information. The proposed adaptive clustering DBIM (AC-DBIM) is compared with three conventional methods (DBIM, multiplicative regularized contrast source inversion (MR-CSI), and CSI for shape and location reconstruction (SL-CSI)) in two-dimensional scenario on a head phantom and numerical head model with different strokes. Three-dimensional simulations are also conducted to indicate the suitability of AC-DBIM in real-life brain imaging. Lastly, the proposed algorithm is assessed using a clinical electromagnetic head scanner developed on phantoms. The simulation and experimental results show superiority of AC-DBIM compared to conventional methods. AC-DBIM achieves significant improvement in the size and shape reconstruction and reduction in errors and standard deviation of the reconstructed εr and σ at clinical scenarios compared with conventional DBIM.

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.

Cross-Correlated Contrast Source Inversion

In this paper, we improved the performance of the contrast source inversion (CSI) method by incorporating a so-called cross-correlated cost functional, which interrelates the state error and the data error in the measurement domain. The proposed method is referred to as the cross-correlated CSI. It enables better robustness and higher inversion accuracy than both the classical CSI and multiplicative regularized CSI (MR-CSI). In addition, we show how the gradient of the modified cost functional can be calculated without significantly increasing the computational burden. The advantages of the proposed algorithms are demonstrated using a 2-D benchmark problem excited by a transverse magnetic wave as well as a transverse electric wave, respectively, in comparison to classical CSI and MR-CSI.

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.

Multiplicative-Regularized FFT Twofold Subspace-Based Optimization Method for Inverse Scattering Problems

In this paper, we combine two techniques together, i.e., the fast Fourier transform-twofold subspace-based optimiza- tion method (FFT-TSOM) and multiplicative regularization (MR) to solve inverse scattering problems. When applying MR to the objective function in the FFT-TSOM, the new method is referred to as MR-FFT-TSOM. In MR-FFT-TSOM, a new stable and effec- tive strategy of regularization has been proposed. MR-FFT-TSOM inherits not only the advantages of the FFT-TSOM, i.e., lower computational complexity than the TSOM, better stability of the inversion procedure, and better robustness against noise compared with the SOM, but also the edge-preserving ability from the MR. In addition, a more relaxed condition of choosing the number of current bases being used in the optimization can be obtained compared with the FFT-TSOM. Particularly, MR-FFT-TSOM has even better robustness against noise compared with the FFT- TSOM and multiplicative regularized contrast source inversion (MR-CSI). Numerical simulations including both inversion of synthetic data and experimental data from the Fresnel data set validate the efficacy of the proposed algorithm.

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.

Microwave Imaging of Human Forearms: Pilot Study and Image Enhancement

We present a pilot study using a microwave tomography system in which we image the forearms of 5 adult male and female volunteers between the ages of 30 and 48. Microwave scattering data were collected at 0.8 to 1.2 GHz with 24 transmitting and receiving antennas located in a matching fluid of deionized water and table salt. Inversion of the microwave data was performed with a balanced version of the multiplicative-regularized contrast source inversion algorithm formulated using the finite-element method (FEM-CSI). T1-weighted MRI images of each volunteer's forearm were also collected in the same plane as the microwave scattering experiment. Initial “blind” imaging results from the utilized inversion algorithm show that the image quality is dependent on the thickness of the arm's peripheral adipose tissue layer; thicker layers of adipose tissue lead to poorer overall image quality. Due to the exible nature of the FEM-CSI algorithm used, prior information can be readily incorporated into the microwave imaging inversion process. We show that by introducing prior information into the FEM-CSI algorithm the internal anatomical features of all the arms are resolved, significantly improving the images. The prior information was estimated manually from the blind inversions using an ad hoc procedure.

Contrast source inversion method applied to relatively high contrast objects

This paper presents a contrast source inversion method for microwave tomography with improved performance with respect to the popular multiplicative regularized contrast source inversion (MR-CSI) method when the contrast of the object under study is relatively high. More precisely, some shortcomings of MR-CSI which may prevent it from performing adequately on higher contrast objects are outlined. The proposed method does not suffer from such shortcomings, but necessitates the tuning of parameters. However, a unique set of parameters can be used in a wide variety of experimental conditions related to a given application. Simple guidelines to determine their values are provided.

Fast Solutions of the 2D Inverse Scattering Problem Based on a TSVD Approximation of the Internal Field for the Forward Model

An alternative formulation of the microwave tomography problem is proposed, in order to reduce the computation time of the inversion procedure. The well-known multiplicative regularized contrast source inversion method is used as reference algorithm. Our formulation is based on a truncated singular value decomposition of the matrix involved in the most computationally intensive operations of the inversion algorithm. After theoretical and practical investigation of the behavior of the singular values, it is shown that the corresponding approximation does not yield any significant degradation of the quality of the solutions even for large complex permittivity contrasts, while the computation times are reduced by a factor ranging between 1.1 and 6 with respect to the original method.

Application of the MR-CSI Method for Three-Dimensional Imaging of the Triaxial Induction Measurements

We present a nonlinear inversion method for 3-D imaging of the near-wellbore region employing multiarray triaxial induction data. The method used is the so-called multiplicative-regularized contrast source inversion method. There are two main features of this method. The first is that the method does not require the explicit solution of the full forward problem at each iteration step. The second is that the regularizer is included as a multiplicative constraint that allows the automatic and adaptive determination of the regularization parameter. These two features enable us to robustly solve a large-scale inverse problem using single-processor present-day computer power.

Optical microscopy imaging using the contrast source inversion method

The reconstruction of the permittivity profile from optical diffraction tomography data is discussed. In order to arrive at sub-100 nm resolution it is necessary to employ nonlinear inversion methods that yield quantitative information of the permittivity distribution. Therefore, the so-called multiplicative regularized contrast source inversion (MRCSI) method is adopted to the problem at hand. For a two-dimensional representative example it is demonstrated that, using a wavelength of 400 nm, resolutions of the order of 20 to 30 nm can be achieved. We show that the MRCSI method is very effective in noisy environments and is able to handle very limited data.

A Wideband Microwave Tomography System With a Novel Frequency Selection Procedure

In this paper, we describe a 2-D wideband microwave imaging system intended for biomedical imaging. The system is capable of collecting data from 3 to 6 GHz, with 24 coresident antenna elements connected to a vector network analyzer via a 2 x 24 port matrix switch. As one of the major sources of error in the data collection process is a result of the strongly coupling 24 coresident antennas, we provide a novel method to avoid the frequencies where the coupling is large enough to prevent successful imaging. Through the use of two different nonlinear reconstruction schemes, which are an enhanced version of the distorted born iterative method and the multiplicative regularized contrast source inversion method, we show imaging results from dielectric phantoms in free space. The early inversion results show that with the frequency selection procedure applied, the system is capable of quantitatively reconstructing dielectric objects, and show that the use of the wideband data improves the inversion results over single-frequency data.

Comparison of an Enhanced Distorted Born Iterative Method and the Multiplicative-Regularized Contrast Source Inversion method

For 2D transverse magnetic (TM) microwave inversion, multiplicative-regularized contrast source inversion (MR-CSI), and the distorted Born iterative method (DBIM) are compared. The comparison is based on a computational resource analysis, inversion of synthetic data, and inversion of experimentally collected data from both the Fresnel and UPC Barcelona data sets. All inversion results are blind, but appropriate physical values for the reconstructed contrast are maintained. The data sets used to test the algorithms vary widely in terms of the background media, antennas, and far/near field considerations. To ensure that the comparison is replicable, an automatic regularization parameter selection method is used for the additive regularization within the DBIM, which utilizes a fast implementation of the L-curve method and the Laplacian regularizer. While not used in the classical DBIM, we introduce an MR term to the DBIM in order to provide comparable results to MR-CSI. The introduction of this MR term requires only slight modifications to the classical DBIM algorithm, and adds little computational complexity. The results show that with the addition of the MR term in the DBIM, the two algorithms provide very similar inversion results, but with the MR-CSI method providing advantages for both computational resources and ease of implementation.

Two-Dimensional Contrast Source Inversion Method With Phaseless Data: TM Case

In this paper, two new approaches are presented for the solution of electromagnetic inverse scattering problems when amplitude-only data are available. The proposed techniques are based on a customized version, which are the so-called contrast source inversion (CSI) and multiplicative regularized CSI (MRCSI) methods. In the proposed approaches, denoted as the phaseless-data (PD)-CSI and the PD-MRCSI, only the term of the cost functional concerning the mismatch between the measured and estimated field data (i.e., the data equation) has been properly redefined. Moreover, the back-projection algorithm has been modified to provide an initial solution ensuring the rapid convergence of the optimization procedures and avoid the reconstruction of false solutions. A set of representative results concerning numerical as well as experimental tests is reported to show the accuracy of the proposed amplitude-only reconstruction approaches.

A multi-frequency MRCSI algorithm with phaseless data

This paper presents a novel multi-frequency multiplicative regularized contrast source inversion (MRCSI) algorithm with phaseless data (PD-MRCSI) for solving a two-dimensional scalar inverse scattering problem. The MRCSI method resolves the inverse scattering problem by minimization of a cost functional which is a linear combination of mismatches in the data equation and the state equation. Through modifying the mismatch in the data equation, we construct a new cost functional which is suitable for the inverse scattering problem with phaseless data. Similar to the MRCSI algorithm, the new cost functional can be minimized by alternatively updating the unknown contrast source and contrast using the so-called Polak–Ribere conjugate gradient method. Numerical results show that the proposed algorithm works effectively and efficiently for solving the inverse scattering problem with phaseless data.

Application of the multiplicative regularized contrast source inversion method on 3D experimental Fresnel data

This paper presents the results of inversion of multi-frequency electromagnetic scattered field data, measured by the Institute of Fresnel, Marseille, France, from three-dimensional (3D) homogeneous objects, both for co-polarization and cross-polarization antenna orientations. The reconstructions were obtained by using the multiplicative regularized contrast source inversion (MR-CSI) method. The inversion results indicated that the MR-CSI is able to robustly and efficiently invert these 3D data sets using minimal a priori information.

Enhancement of microwave tomography through the use of electrically conducting enclosures

We consider microwave tomography (MWT) where the imaging region is surrounded by an electrically conducting surface. This surface acts as both a shield from outside interference, holding tank for any possible matching media, and, in certain cases, serves to enhance the performance of electromagnetic (EM) inversion algorithms. For the 2D transverse magnetic (TM) case and where the surface consists of a perfect electrical conductor (PEC) in the shape of a circular cylinder, we formulate an appropriate Greens function which is amenable to implementation in the existing EM inversion codes. We utilize this Greens function in the multiplicative-regularized contrast source inversion (MR-CSI) method. Several different synthetic examples are used to test the performance of the inversion when the PEC surface is present and the results show that in many cases, the tomographic image is significantly improved. The reasons for the improved inversion results are an area of active research, but are likely to be due to the increased interrogation energy deposited into the imaging region. Results are also shown which demonstrate the problems which may arise if the unbounded domain Greens function is used in an MWT system that utilizes a matching medium of finite extent—a problem which is overcome by the inclusion of a PEC surface on the exterior of the MWT system.

An integral equation approach for 2.5-dimensional forward and inverse electromagnetic scattering

SUMMARY We present 2.5-D forward and inverse algorithms for modelling low-frequency electromagnetic scattering problems. These algorithms are intended to be used for interpretation of large-scale electromagnetic geophysical data. The algorithms are based on an integral equation approach. To solve the forward problem, a standard conjugate gradient normal residual method is employed, while the inverse problem is solved with the so-called multiplicative regularized contrast source inversion method. Inversion results with low-frequency electromagnetic data for single- and cross-well configurations are presented. Furthermore the advantages of combining the long-offset single-well and cross-well data are discussed.

NONLINEAR INVERSION OF MULTI-FREQUENCY MICROWAVE FRESNEL DATA USING THE MULTIPLICATIVE REGULARIZED CONTRAST SOURCE INVERSION

This paper presents the results of profile inversion of multi-frequency electromagnetic scattered field data, measured by the Institute Fresnel, Marseille, France, from cylindrical objects, both for TM and TE illuminations. The reconstructions are obtained by applying the Multiplicative Regularized Contrast Source Inversion (MR-CSI) method. The results show that the MR-CSI method successfully performs 'blind' inversion of a wide class of scattered field data. Further, we also show that by inverting both TM and TE data simultaneously, a more accurate reconstructed image can be obtained.