Forward-Backward Time-Stepping Research Articles

An Efficient of Overlapping Grid Method with Scattering Technique in Time Domain for Numerical Modeling

An Overlapping Grid Method (OGM) with Biquadratic Spline Interpolation in scattering technique was developed to solve the direct and inverse scattering issues. A two-dimensional (2D) numerical image model was used to analyze the accuracy of the proposed method in a direct scattering process. It was discovered that when the sub-grid, sx ∆ increased, the absolute error for the electric field amplitude will also increase. The results also discovered that as the grid size ratio increased, the absolute error of the amplitude Z E will also increase. The findings show that smaller grid spacing and a finer grid size can produce more accurate results. The Overlapping Grid Method (OGM) with Biquadratic Spline Interpolation was expanded by incorporating with Forward-Backward Time Stepping (FBTS) technique to solve inverse scattering issues. Homogenous embedded objects with a square and circular shape are used to validate the efficiency of the proposed method. The findings showed that the proposed numerical method could detect and reconstruct embedded objects in different shapes. The efficiency of the proposed method was examined by Mean Square Error (MSE) and normalizing the functional error. The findings revealed that the MSE of dielectric profiles for the proposed method were lower than the FDTD method in FBTS. The relative permittivity and conductivity profile differed by 27.06% and 20%, respectively. Hence, it was proven that the proposed method successfully solved a known drawback to the FDTD method and produced more accurate and efficient results.

Hybrid Approaches in Microwave Imaging Using Quantitative Time- and Frequency-Domain Algorithms

In this work we propose two hybrid time-and frequency-domain microwave imagingschemes aimed to improve time-to-solution of quantitative time-domain imaging algorithms and image resolution of quantitative frequency-domain imaging algorithms. The proposed hybrid methods combine discontinuous Galerkin method (DGM) implementations of the time-domain (TD) forward-backward time-stepping (FBTS) algorithm and the frequency-domain (FD) contrast source inversion (CSI) or Gauss Newton Inversion (GNI). Simply put, an initial inversion in one domain (time or frequency) is used as prior information for the other. These schemes, referred to as FD-TD when FD prior is used in a TD algorithm, and TD-FD when TD prior is used in a FD algorithm, are applied to experimental and synthetic data. The results of the hybrid imaging approaches manifest an appreciable improvement relative to the stand-alone of FD and TD algorithms. Specifically, this study demonstrates that low-resolution frequency-domain prior information improves TD convergence. Additionally, we show that early-iteration time-domain solutions improves FD algorithm performance. We hope that these hybridization techniques pave the way for future investigations of optimal strategies for combining TD and FD schemes.

An Efficient of Chimera Grid Scheme with Spline Interpolation in FBTS Inversion Technique for Extremely Dense Breast Cancer Detection

Microwave imaging system is classified as non-invasive, simple to perform and inexpensive compared to MRI and X-Ray machine. Therefore, the novel idea of this research work is to develop a Chimera Grid Scheme (CGS) incorporate with the microwave inverse scattering technique in a low cost, non-ionising and safe short-range. The CGS with spline interpolation in Forward Backward Time-Stepping (FBTS) inversion technique can determined an accurate result especially for the biological anomalies like breast tumours at an early curable stage due to the high electrical properties contrast between malignant cells and normal cells. The findings showed that the proposed method successfully detected and reconstructed the breast structure in relative permittivity profiles. The quantitative information of reconstructed images, such as location, shape, size and internal composition also can be obtained. Furthermore, the normalised functional error for proposed method was also lower than the FDTD method in FBTS. At 150th iteration, the difference of normalised functional error between these two methods was 1.74 × 10−5. The result shows that the CGS method in FBTS inversion technique would reconstruct breast composition more precisely.

Breast Tumour Identification based on Chimera Overset Grid with Spline Interpolation in Forward-Backward Time-Stepping

Active microwave imaging (MI) technique has been recently recommended as a new technology for early detection of malignant breast tumours. Finite-difference Time-domain (FDTD) method is an effective numerical tool for computational electrodynamics modelling. However, the main drawback of the FDTD method is difficult to model the curved boundaries and small features of arbitrary shaped fibroglandular region due to its restriction to inherent orthogonal grids. To address this issue, Chimera Overset Grid (COG) method with spline interpolation in Forward-Backward Time-Stepping (FBTS) inverse scattering technique was proposed to overcome the limitation of FDTD method. In order to analyse the accuracy of this new method to detect a malignancy tumour embedded in different classes of breast parenchymal density, the homogeneous mostly fatty breast and extremely dense breast were chosen as Case A, and Case B, respectively. The Mean Squared Error (MSE) and normalised cost error functional for reconstructed dielectric profiles utilising the proposed method achieved significantly lower values than the FDTD method in FBTS inverse scattering. The results indicated that the proposed method could accurately identify malignancy tumour location and reconstruct the breast composition in dielectric profiles.

A Comparison of Time-Domain and Frequency-Domain Microwave Imaging of Experimental Targets

An existing forward-backward time-stepping (FBTS) time-domain quantitative imaging algorithm is augmented with a discontinuous Galerkin method (DGM) forward solver. The resulting DGM-FBTS imaging algorithm is capable of solving the electromagnetic inverse scattering problem using high-order expansions of the fields and unknown target constitutives, decoupling the solution from the unstructured grid. DGM-FBTS provides a time-domain alternative to our previous development of flexible DGM-based frequency-domain imaging codes, and enables us to present a comparison of the performance of time-domain and frequency-domain imaging algorithms for synthetic and experimental targets. For experimental targets, a procedure for obtaining calibrated time-domain data from frequency-domain broadband VNA-collected data is explained and applied to a system with a reduced number of transmitters and receivers to highlight the potential benefits of time-domain methods. Results highlight the potential capabilities of time-domain experimental imaging using the same hardware configuration used to collect broadband frequency-domain measurements and suggest future work on hybrid frequency- and time-domain imaging algorithms and efforts to improve the computational performance of DGM-FBTS.

Overset grid generation with inverse scattering technique for object and crack detection

This paper presents the forward backward time stepping (FBTS) technique with finite difference time domain (FDTD) method and overset grid generation (OGG) method was applied for the reconstruction of object and crack detection. Object and crack detection is widely used in structural health monitoring (SHM) application especially in civil structure to detect the buried object and also cracks. The proposed numerical approach has been validated by investigating different kind of ratio of grid size between the main mesh and sub-mesh. Then, the proposed numerical approach is implemented in the analysis of the detection of objects such as concrete blocks and cracks underground. Here, the numerical errors between the actual result and simulated result had been calculated by using relative error. It is shown that the proposed approach has 5.22% error and nearer to the actual value.

AUTOMATED SCALING REGION OF INTEREST WITH ITERATIVE EDGE PRESERVING IN FORWARD-BACKWARD TIME-STEPPING

The thesis reported on a deterministic inverse scattering method in time-domain to reconstruct dielectric profiles of an unknown embedded object within its peripheral region. Image reconstruction of geometrically simple objects taken after breast profiles and lung(s) model are solely done by simulation executed in single computing. In effort to alleviate the nonlinearity problem of inverse scattering, the inversion technique has been integrated with varied types of techniques to improve the inversion solution. The extended algorithm would only increase the computational cost, nevertheless would never eliminate the nonlinearity problem that degrade the inversion solution. The reconstruction process started in a coarse region which then rescaled down according to object geometry configuration. This is accomplished by combining an inversion technique of Forward-Backward Time-Stepping (FBTS) with an Automated Scaling Region of Interest (AS-ROI) method. Edge preserving techniques comprises of edge preserving regularization and anisotropic diffusion are integrated into the combined FBTS and AS-ROI to further increase the accuracy level in the profiles’ intensity. Accuracy of reconstructed object is validated by using mean squared error (MSE), relative error (RE) and Euclidean distance (ED) that measure the precision in terms of pixels’ intensity, size and localization. Results exhibited significant improvement in the accuracy level of reconstructed images with a combined method of FBTS and AS-ROI. AS-ROI has successfully increased the pixels precision in relative to FBTS about 10.33% for breast model and 25.17% for lung model. The accuracy increment by AS-ROI is due to better fields penetration as exterior pixels are replaced with background layer of low profiles. In the combined rescaled and regularized method in FBTS, edge preserving smoothing filter and regularization are alternately imposed on the improved reconstructed profiles by AS-ROI. Therefore, the accuracy is further increased to 18.58% and 40.68%, respectively for breast and lung model. In term of size estimation, average error in object’s radius is analogous to accuracy level measured in MSE. It indicates that efficiency of AS-ROI is highly relied upon the accuracy of FBTS estimation in reconstructing image profiles prior to rescaling process. Apart from that, accuracy in size estimation differ for varied shapes due to number of pixels at the boundary. Average RE is 61.94% for a circular shape in breast model, meanwhile attains RE of 4.17% for a U-shape object. The highest RE for a single circular tumour’s size in lung model is 62.5%. However, object localization by AS-ROI is 100% for a circular and U-shape object in breast model. Nevertheless, AS-ROI attains an average ED of 2.3 for lung model. Computational time decreases accordingly with the reduced number of pixels involved after the rescaling process. Reduction in the computational time is 13.06% for breast model, nonetheless 28.74% for lung model. Significant time reduction observed for lung model is benefited from considerable number of pixels that has been removed from the original image. The inclusion of edge preserving techniques into the combined AS-ROI with FBTS however has slightly increase the computational time about 5.87% and 4.69% for breast and lung model, respectively. Nevertheless, it compensates the computational cost for higher accuracy of image profiles’ intensities.

Image Reconstruction Based on Combination of Inverse Scattering Technique and Total Variation Regularization Method

<p>The Forward-Backward Time-Stepping (FBTS) had proven its potential to reconstruct images of buried objects in inhomogeneous medium with useful quantitative information about its size, shape, and locality. The Total Variation regularization method was incorporated with the FBTS algorithm to deal with the ill-posedness or ill-conditionedness of the inverse problem. The effectiveness of the proposed technique is confirmed by numerical simulations. The numerical method was carried out on a simple object detection through FBTS with and without TV regularization method. The detection and reconstruction of relative permittivity and conductivity of the simple object have shown an improvement as TV regularization method applied whereas it smoothed the vibrations of the images and gave a better estimation of the image’s boundaries.</p>

A New Approach for Solving Inverse Scattering Problems with Overset Grid Generation Method

This paper presents a new approach of Forward-Backward Time-Stepping (FBTS) utilizing Finite-Difference Time-Domain (FDTD) method with Overset Grid Generation (OGG) method to solve the inverse scattering problems for electromagnetic (EM) waves. The proposed FDTD method is combined with OGG method to reduce the geometrically complex problem to a simple set of grids. The grids can be modified easily without the need to regenerate the grid system, thus, it provide an efficient approach to integrate with the FBTS technique. Here, the characteristics of the EM waves are analyzed. For the research mentioned in this paper, the ‘measured’ signals are syntactic data generated by FDTD simulations. While the ‘simulated’ signals are the calculated data. The accuracy of the proposed approach is validated. Good agreements are obtained between simulation data and measured data. The proposed approach has the potential to provide useful quantitative information of the unknown object particularly for shape reconstruction, object detection and others.

PROFILE RECONSTRUCTION UTILIZING FORWARD-BACKWARD TIME-STEPPING WITH THE INTEGRATION OF AUTOMATED EDGE-PRESERVING REGULARIZATION TECHNIQUE FOR OBJECT DETECTION APPLICATIONS

A regularization is integrated with Forward-Backward Time-Stepping (FBTS) method which is formulated in time-domain utilizing Finite-Difference Time-Domain (FDTD) method to solve the nonlinear and ill-posed problem arisen in the microwave inverse scattering problem. FBTS method based on a Polak-Ribiete-Polyak conjugate gradient method is easily trapped in the local minima. Thus, we extend our work with the integration of edge-preserving regularization technique due to its ability to smooth and preserve the edges containing important information for reconstructing the dielectric profiles of the targeted object. In this paper, we propose a deterministic relaxation with Mean Square Error algorithm known as DrMSE in FBTS and integrate it with the automated edge-preserving regularization technique. Numerical simulations are carried out and prove that the reconstructed results are more accurate by calculating the edge-preserving parameter automatically.

Preliminary Results of Integrating Tikhonov’s Regularization in Forward-Backward Time-Stepping Technique for Object Detection

The inverse scattering in time domain known as Forward-Backward Time-Stepping (FBTS) technique is applied to determine the sizes, shape and location of the embedded objects. Tikhonov’s regularization method has been proposed in order to improve or solve the ill-posed of FBTS inverse scattering problem. The reconstructed results showed that FBTS technique can detect the presence of embedded objects. The reconstructed results of FBTS technique utilizing with the Tikhonov’s regularization method shown better results than the results only applied FBTS technique. Tikhonov’s regularization combined with FBTS technique to improve the quality of image reconstruction.

Elliptic Filter and Iterative Inversion Method for Buried Object Detection Applications

In this paper, Forward-Backward Time-Stepping (FBTS) inversion method is used for detection, imaging and reconstruction of an unknown object in a region of interest. We consider the reconstruction parameter profiles of two-dimensional objects from measurement of the transient total electromagnetic field data contaminated with noise. A preliminary result of an Elliptic filter integrated in FBTS algorithm to suppress noise effect has been obtained. A circular shape in the region of interest is successfully detected and reconstructed.

PRELIMINARY RESULTS ON ESTIMATION OF THE DISPERSIVE DIELECTRIC PROPERTIES OF AN OBJECT UTILIZING FREQUENCY-DEPENDENT FORWARD-BACKWARD TIME-STEPPING TECHNIQUE

In this paper, a Frequency-Dependent Forward-Backward Time-Stepping (FD-FBTS) inverse scattering technique is used for reconstruction of homogeneous dispersive object. The aim of the technique is to reconstruct the relative permittivity at infinite frequency, static relative permittivity and static conductivity of the homogeneous dispersive object simultaneously. The technique utilizes iterative finite-difference time-domain (FDTD) method for solving inverse scattering problem in time domain. The minimization of the cost functional is carried out utilizing Dai-Yuan nonlinear conjugate-gradient algorithm. The Frechet derivatives of the augmented cost functional are derived analytically with respect to scatterer properties. Numerical results for reconstruction of two-dimensional homogeneous dispersive illustrate the performance of the proposed technique.

CHEBYSHEV FILTER APPLIED TO AN INVERSION TECHNIQUE FOR BREAST TUMOUR DETECTION

Microwave imaging has been extensively studied in the past several years as a new technique for early stage breast cancer detection. The rationale of microwave imaging for breast tumour detection is significant contrast in the dielectric properties of normal tissue and malignant tumours. However, in practice noise present from the environments during screening/examination degrades the quality of the image. Inaccurate reconstructed image caused false/misleading interpretation of the image which leads to inappropriate diagnose or treatment to the patient. In the simulation works, noise is added to imitate the actual environment scenario. The two-dimensional (2D) object that identical to breast model is developed using numerical simulation to imitate the breast model. A filter is integrated with an iterative inversion technique for breast tumour detection to eliminate the noise. To assess the effectiveness of this approach, we consider the reconstruction of the electrical parameter profiles of 2D objects from measurements of the transient total electromagnetic field data contaminated with noise. Additive white Gaussian noise is utilized to mimic the effect of random processes that occur in the nature. This paper presents the filter settings and characteristics that affect the reconstruction of the image in order to obtain the most reliable and closer to the actual image. Selection of filter settings or design is important in order to achieve desired signal, most accurate image and provide reliable information of the object. Chebyshev low pass filter is applied in the Forward-Backward Time-Stepping (FBTS) algorithm to filter the noisy data and to improve the quality of reconstructed image.

Increasing waveform inversion efficiency of GPR data using compression during reconstruction

We propose a method to avoid large amounts of data storage and reading during the reconstruction of a forward–backward time-stepping (FBTS) method for ground-penetrating radar (GPR) data using compression and decompression. The reconstruction example shows that the reconstruction result is acceptable if the compression ratio is less than 90%.

Advances in the 3-D Forward–Backward Time-Stepping (FBTS) Inverse Scattering Technique for Breast Cancer Detection

This paper presents recent advances in a 3-D inverse scattering technique, called forward-backward time-stepping (FBTS), applied to the reconstruction of the microwave properties of the breast. The FBTS algorithm is utilized for a numerical-based study of a 3-D breast model based on an MRI. Several illumination schemes, based on different microwave transmitter/receiver configurations, are compared based on the quality of the reconstructed images of the breast model. A combination of cylindrical and planar arrays is shown to provide accurate estimates of the model electrical parameters that delineate the various regions of the breast. Although further analysis with this combination array demonstrates that tumors of reduced size and reduced contrast with the surrounding fibroglandular region are much more difficult (and in some cases not possible) to reconstruct, the study presents some promising initial results of a reconstruction technique for breast imaging and cancer detection.

Two-Dimensional Time-Domain Inverse Scattering for Quantitative Analysis of Breast Composition

Forward-backward time-stepping is a unique approach for solving electromagnetic inverse scattering problems in the time domain. In this paper, the technique is applied to a realistic, heterogeneous breast model. The ability to detect a 5-mm diameter malignancy and provide substantial quantitative information about the breast's composition is demonstrated.

Parallel Processing of Forward-backward Time-stepping Method for Time Domain Inverse Scattering

Parallel computing is applied to FBTS method, which is one of the solution methods of time domain inverse scattering problem, to shorten the calculation time. A cluster of 8 PCs is constructed and parallel processing is realized using MPI. A 3-D reconstruction of wooden hollow cylinder from the experimental data is examined by parallel FBTS algorithm. It is shown that the parallel processing reduces the calculation time and FBTS algorithm provides proper reconstructed proflles of target with respect to relative permittivity and conductivity. Electromagnetic wave inverse scattering problem are investigated in various flelds such as medi- cal imaging, geophysical exploration, nondestructive testing, and target identiflcations (1{6). We have proposed a time-domain inverse scattering imaging technique, the forward-backward time- stepping (FBTS) method, to reconstruct the electrical parameter proflles of scattering objects. It was clarifled that quite good reconstructed results were obtained using the FBTS method in several numerical simulations (7). We also showed its usefulness in real situations by applying the FBTS method to experimental data (8). Although the FBTS method is efiective to inverse scattering prob- lems, the computation time is quite long to get accurate results in dealing with three-dimensional (3-D) objects. Therefore reconstruction processing time in the FBTS method is required to be greatly reduced. In this paper, we investigate the reduction of the computation time of the FBTS method by introducing parallel processing of the method. In the FBTS method, it is necessary that the same number of direct and adjoint scattering problems as that of transmitter points are calculated in order to obtain the gradient vector which is related to the update of the estimation for electrical parameters (1{4). We construct a cluster of 8 personal computers and implement a parallel algo- rithm for FBTS method using Message Passing Interface (MPI) library. Since the calculation of direct and adjoint problems is conducted simultaneously by several computers, parallel FBTS algo- rithm is expected to reduce the computation time. The experiment to acquire the measured data of a wooden hollow cylinder by circular array antenna in cross sectional slices is carried out, and 3-D reconstruction of the target is examined by proposed parallel FBTS method. In the following sections, the FBTS algorithm, parallel method and reconstruction results are shown. 2. FBTS ALGORITHM Maxwell's equations in the matrix form is given by

Source-group method to speed up the reconstruction of objects from radar data by using the FBTS method

We have proposed a time-domain forward-backward time-stepping (FBTS) method for reconstructing 3D structures in highly absorptive media. The reconstruction speed is greatly dependent on the number of transmitters. In this paper, we propose a source-group method to speed up the reconstruction. In the source-group method, multiple transmitters arranged at different positions are excited simultaneously, and receivers collect the wave fields. To compare the reconstruction results, three kinds of reconstructions from 16 conventional single transmitter-multiple receiver data sets, four source-group multiple-receiver data sets, and four conventional single-transmitter multiple-receiver data sets are carried out. Reconstruction by the source-group method is several times faster than (and the reconstructed results are almost the same as) those of the first kind of reconstruction, and they are much better than those of the third kind. © Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 67–71, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21263

FILTERED FORWARD-BACKWARD TIME-STEPPING METHOD APPLIED TO RECONSTRUCTION OF DIELECTRIC CYLINDERS

In this paper, an optimization approach for reconstructing the electrical parameters of cylindrical objects from total field data in the time domain is examined. Noise in measured field data degrades the quality of reconstructed image based on the forward-backward time-stepping (FBTS) algorithm previously proposed. In order to improve the image quality, we propose a new reconstruction algorithm. The measured time domain data are low-pass filtered and the FBTS algorithm is used for the filtered data. Numerical simulations are carried out to show the effectiveness of this algorithm for a high-contrast object.