Born Iterative Method Research Articles

Enhanced Machine Learning Approach for Accurate and Fast Resolution of Inverse Scattering Problem in Breast Cancer Detection

An improved machine learning approach is presented in this paper to guarantee the fast convergence of the Born Iterative Method, even in the presence of strong scatterers, by assuming a single operating frequency and a reduced number of antennas in the scattering setup. The initial estimation of the dielectric profile, provided by the Born Iterative Method, was processed by a specific convolutional neural network to improve the reconstruction using a fast machine learning approach. To ensure rapid convergence, a proper choice of the initial guess in terms of the minimum permittivity value over the entire domain was also made. Numerical validations on realistic breast phantoms were illustrated, demonstrating an average error of 2.4% and an accuracy greater than 96% for all considered tests, even when considering a single operating frequency and a reduced amount of training data.

Machine Learning Approach to Quadratic Programming-Based Microwave Imaging for Breast Cancer Detection.

In this work, a novel technique is proposed that combines the Born iterative method, based on a quadratic programming approach, with convolutional neural networks to solve the ill-framed inverse problem coming from microwave imaging formulation in breast cancer detection. The aim is to accurately recover the permittivity of breast phantoms, these typically being strong dielectric scatterers, from the measured scattering data. Several tests were carried out, using a circular imaging configuration and breast models, to evaluate the performance of the proposed scheme, showing that the application of convolutional neural networks allows clinicians to considerably reduce the reconstruction time with an accuracy that exceeds 90% in all the performed validations.

Calibrated Frequency-Division Distorted Born Iterative Tomography for Real-Life Head Imaging.

The clinical use of microwave tomography (MT) requires addressing the significant mismatch between simulated environment, which is used in the forward solver, and real-life system. To alleviate this mismatch, a calibrated tomography, which uses two homogeneous calibration phantoms and a modified distorted Born iterative method (DBIM), is presented. The two phantoms are used to derive a linear model that matches the forward solver to real-life measurements. Moreover, experimental observations indicate that signal quality at different frequencies varies between different antennas due to inevitably inconsistent manufacturing tolerance and variances in radio-frequency chains. An optimum frequency, at which the simulated and measured signals of the antenna present maximum similarity when irradiating the calibrated phantoms, is thus calculated for each antenna. A frequency-division DBIM (FD-DBIM), in which different antennas in the array transmit their corresponding optimum frequencies, is subsequently developed. A clinical brain scanner is then used to assess performance of the algorithm in lab and healthy volunteers' tests. The linear calibration model is first used to calibrate the measured data. After that FD-DBIM is used to solve the problem and map the dielectric properties of the imaged domain. The simulated and experimental results confirm validity of the presented approach and its superiority to other tomographic method.

Distorted Born iterative method with back-propagation improves permittivity reconstruction

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

Fractional Regularized Distorted Born Iterative Method for Permittivity Reconstruction

Fractional Regularized Distorted Born Iterative Method for Permittivity Reconstruction

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.

Three-Dimensional Microwave Head Imaging with GPU-Based FDTD and the DBIM Method.

We present a preliminary study of microwave head imaging using a three-dimensional (3-D) implementation of the distorted Born iterative method (DBIM). Our aim is to examine the benefits of using the more computationally intensive 3-D implementation in scenarios where limited prior information is available, or when the target occupies an area that is not covered by the imaging array’s transverse planes. We show that, in some cases, the 3-D implementation outperforms its two-dimensional (2-D) counterpart despite the increased number of unknowns for the linear problem at each DBIM iteration. We also discuss how the 3-D algorithm can be implemented efficiently using graphic processing units (GPUs) and validate this implementation with experimental data from a simplified brain phantom. In this work, we have implemented a non-linear microwave imaging approach using DBIM with GPU-accelerated FDTD. Moreover, the paper offers a direct comparison of 2-D and 3-D microwave tomography implementations for head imaging and stroke detection in inhomogenous anatomically complex numerical head phantoms.

Reconstruction of three-dimensional objects in layered composite structures from multimode orbital angular momentum.

Because of helical phase wavefront distribution, vortex electromagnetic waves are considered to carry more information and additional degrees of freedom than traditional spherical waves. Therefore, a vortex wave carrying orbital angular momentum (OAM) can improve inversion and imaging accuracy. In this work, we revisit the reconstruction of three-dimensional objects in layered composite structures extended with OAM. In forward modeling, the concentric uniform circle array is used to generate electromagnetic vortex beams. To analyze the difference of vortex beams, the electric field radiation pattern and phase pattern distribution of OAM waves with different modes are calculated. Then, the scattered field of layered media illuminated by different OAM beams is determined by the dyadic Green's function and the stabilized biconjugate gradient technique with a fast Fourier transform algorithm. In the inversion, the variational Born iterative method is used to reconstruct targets in layered composite structures, and multiple OAM modes are used to improve the reconstruction results. The numerical results prove that the permittivity of the target can be better reconstructed by using the multiple OAM modes rather than the traditional spherical wave. With the increase of OAM mode number, the reconstructed target parameters are closer to the true value. We expect that our results will provide a better understanding of the OAM and pave the way for the improvement of inversion and optical imaging technology using vortex waves.

Hybrid Microwave Imaging of 3-D Objects Using LSM and BIM Aided by a CNN U-Net

This paper presents an efficient and accurate three-dimensional (3-D) quantitative hybrid microwave imaging method. The linear sampling method (LSM) is first carried out to quickly find the approximate shapes and locations of the unknown objects in the imaging domain based on the scattered field data recorded by receivers which are placed in the far-field zone and wrap the domain. Then the full-wave inversion (FWI) is implemented in a downsized domain which tightly encloses the unknown objects instead of in the whole domain through the Born iterative method (BIM) to quantitatively retrieve the dielectric model parameters of the objects. Because the LSM fails to obtain the sufficiently accurate shapes of the unknown objects, a trained 3-D CNN U-Net is inserted between the LSM imager and the BIM solver to further refine the obtained shapes of LSM, which is expected to aid the following FWI. The proposed hybrid method is validated via the quantitative imaging of both inhomogeneous isotropic scatterers and multiple homogeneous anisotropic scatterers. It is shown that the hybrid method can achieve both higher reconstruction accuracy and lower computational cost compared with the direct BIM inversion. Meanwhile, its antinoise ability is also tested.

Reconstruction of Subsurface Objects by LSM and FWI From Limited-Aperture Electromagnetic Data

This article presents a hybrid 3-D electromagnetic (EM) full-wave inversion (FWI) method for the reconstruction of subsurface objects illuminated by an antenna array with the limited aperture. The 3-D linear sampling method (LSM) is first used to qualitatively reconstruct the rough shapes and locations of the subsurface objects. Then, the 3-D convolutional neural network (CNN) U-Net is used to further refine the images of the unknown objects. Finally, the Born iterative method (BIM) is implemented to quantitatively invert for the dielectric parameters of subsurface inhomogeneous objects or multiple homogeneous objects in the restricted image regions. Numerical simulations show that, compared with the pure FWI method BIM, the proposed hybrid method can reconstruct subsurface 3-D objects from limited-aperture EM data with both higher accuracy and lower computational cost. In addition, the proposed hybrid method also shows a strong antinoise ability for the reconstruction of multiple subsurface objects.

3-D Voxel-Based Reconstruction of Multiple Objects Buried in Layered Media by VBIM Hybridized With Unsupervised Machine Learning

This article presents a novel hybrid electromagnetic inversion method. The traditional 3-D variational Born iterative method (VBIM) is combined with the unsupervised machine-learning expectation maximization (EM). In each iteration, VBIM first outputs the pseudo-randomly distributed model parameters in all discretized cells in the inversion domain. Then the EM algorithm is used to classify them and estimate the mean model parameter values of each homogeneous scatterer or subscatterer supposing that the reconstructed model parameters in all cells comply with the Gaussian mixture model (GMM). At last, partial cells in the inversion domain classified as “background” will be removed and the unknowns in the next VBIM iteration are reduced. This process is implemented iteratively until no “background” cell can be removed anymore and the data misfit between the measured scattered field and reconstructed field reaches the stop criterion. Finally, the mean value of the model parameter estimated by EM is mandatorily assigned for each homogeneous scatterer or subscatterer. Numerical examples show that the proposed hybrid method works efficiently for the reconstruction of isotropic, anisotropic, homogeneous, or inhomogeneous scatterers. It also has a certain antinoise ability.

Experimental Validation of the DBIM-TwIST Algorithm for Brain Stroke Detection and Differentiation Using a Multi-Layered Anatomically Complex Head Phantom

We present an experimental validation of the distorted Born iterative method with the two-step iterative shrinkage thresholding (DBIM-TwIST) algorithm for the problem of brain stroke detection and differentiation, using an anatomically accurate, multi-layer head phantom. To this end, we have developed a gelatine-based, anatomically complex head phantom which mimics various brain tissues and also includes a target mimicking hemorrhagic or ischemic stroke. We simulated the model and setup using CST Microwave Studio and then used our experimental imaging setup to collect numerical and measured data, respectively. We then used our DBIM-TwIST algorithm to reconstruct the dielectric properties of the imaging domain for both simulated and measured data. Results from our CST simulations showed that we are able to locate and reconstruct the permittivity of different stroke targets using an approximate initial guess. Our experimental results demonstrated the potential and challenges for successful detection and differentiation of the stroke targets.

Experimental Validation of Microwave Imaging Prototype and DBIM-IMATCS Algorithm for Bone Health Monitoring

The evaluation of the microwave imaging (MWI) prototype and imaging algorithms on experimental bone phantoms is a precursor step before clinical testing for measuring <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in vivo</i> dielectric properties of human bones. To this end, this paper presents microwave tomographic image reconstruction of experimental phantoms of normal and diseased human calcaneus bone using an MWI prototype and distorted Born iterative method (DBIM) algorithm for bone health monitoring application. A two-layered simplified cylindrical-shaped 3-D printed phantom was used to mimic the human calcaneus bone. The external and internal layers of the bone phantom mimic the cortical bone and trabecular bone, respectively. Liquid tissue-mimicking mixtures (TMM) for normal bone, osteoporotic bone, and osteoarthritis bone were prepared. The phantoms were placed in the imaging prototype and the electromagnetic inverse scattering problem was solved using the DBIM to create the complex permittivity images. An <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{2}$ </tex-math></inline-formula> -based regularization approach was adopted along with the iterative method with adaptive thresholding for compressed sensing (IMATCS) to overcome the ill-posedness and to solve the underdetermined set of linear equations at each DBIM iteration. The reconstruction of dielectric properties of bone phantoms have shown that <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{2}$ </tex-math></inline-formula> -IMATCS approach provides a robust reconstruction of diverse bone phantoms with acceptable accuracy. Moreover, the osteoporotic and osteoarthritis bone phantoms were distinguished based on reconstructed dielectric properties with an average percentage difference of 26% at 3 GHz. This paper has made the first attempt to validate an MWI prototype for bone imaging application. A DBIM-based iterative method has been employed to classify normal and diseased bone phantoms.

Quantitative Electromagnetic Inversion of Irregular Scatterers Based on a Threefold Hybrid Method

This article presents a threefold hybrid electromagnetic inversion method that combines the linear sampling method (LSM), the convolutional neural network (CNN), and the full-wave inversion (FWI). The whole inversion procedure includes three steps. First, the LSM qualitatively reconstructs the preliminary shapes and locations of the scatterers. Then, the CNN U-Net is used to further refine the shapes of the scatterers. At last, the Born iterative method (BIM) is implemented to quantitatively invert for the permittivity and conductivity of inhomogeneous scatterers or multiple homogeneous scatterers inside the downsized inversion domain. Numerical experiments show that compared with the pure FWI method BIM, the proposed hybrid method can achieve both higher reconstruction accuracy and lower computational cost. Besides this superiority, the proposed hybrid method also has strong adaptability to multiple scatterers with high contrasts even when the measured field data are contaminated by large noise. Laboratory experimental data are also used to verify the feasibility of the proposed method.

Resolution Enhanced Distorted Born Iterative Method Using ROI Limiting Scheme for Microwave Breast Imaging

This paper presents a high-resolution inverse scattering approach using the distorted Born iterative method (DBIM) by utilizing a region-of-interest limitation scheme that assumes microwave breast cancer imaging modality. The DBIM-based tomography approach provides a quantitative dielectric profile, contributing to reliable cancer recognition, especially for dense breast media. However, if the inversion cell is small, the original DBIM will be inaccurate because the unknowns will far exceed the number of data samples. Thus, high-resolution reconstruction is a challenging issue and is not unique only to the DBIM. To address this difficulty, this paper introduces a region-of-interest (ROI)-limited scheme by developing low-resolution DBIM images. Numerical tests based on 2D FDTD demonstrate that the proposed approach provides high-resolution and accurate dielectric profiles for highly heterogeneous realistic phantoms.

Super-Resolution 3-D Microwave Imaging of Objects With High Contrasts by a Semijoin Extreme Learning Machine

This article proposes a semijoin extreme learning machine (SJ-ELM) for super-resolution 3-D microwave imaging of objects with high contrasts. The proposed scheme develops a shallow neural network structure with the semijoin strategy to convert the scattered field data into two output channels, namely, the permittivity and the conductivity of objects, respectively. The semijoin strategy can decrease the inner matrix dimensions to reduce the computational burden for 3-D super-resolution imaging, so it is employed to connect between the nodes of the hidden layer and the output layer. The imaging performance of the proposed SJ-ELM and the conventional variational Born iterative method (VBIM) is first compared for imaging objects with different electrical sizes and contrasts, and then, different targets of imaging resolution are designed to evaluate both solvers. The proposed SJ-ELM is also assessed for imaging objects with high contrasts and experimental data and is demonstrated to have superior super-resolution imaging capabilities for high-contrast 3-D objects.

An Enhanced Multi-Frequency Distorted Born Iterative Method for Ultrasound Tomography Based on Fundamental Tone and Overtones

Conventional Distorted Born Iterative Method (DBIM) using single frequency has low resolution and is prone to creating images with high-contrast subjects. We propose a productive frequency combination method to better result in tomographic ultrasound imaging based on the multi-frequency technique. This study uses the natural mechanism of emitting oscillators' frequencies and uses these frequencies for imaging in iterations. We use a fundamental tone (i.e., the starting frequency f0) for the first iteration in DBIM, then consecutively use its overtones for the next ones. The digital simulation scenarios are tested with other multi-frequency approaches to prove our method's feasibility. We performed 57 different simulation scenarios on the use of multi-frequency information for the DBIM method. As a result, the proposed method for the smallest normalization error (RRE = 0.757). The proposed method's imaging time is not significantly longer than the way of using single frequency information.

Influence of the multi-resolution technique on tomographic reconstruction in ultrasound tomography

The greatest advantage of scattering theory-based ultrasound tomography (UT) is its ability to investigate small structures. DBIM is the Distorted Born Iterative Method. The nearest neighbour interpolation method is used to enhance the reconstruction performance and reduce the reconstruction time. The raw (N 1 × N 1) and dense (N 2 × N 2) meshed integration areas are reconstructed in NN 1 and NN 2 iterations, respectively. However, choosing the best value of NN 1 to get the highest performance was not mentioned in previous works. If it is not well chosen, the reconstruction quality is even worse than that when using no interpolation. This study proposes a method to enhance the UT reconstruction by using the nearest neighbour interpolation (MR-DBIM). The corresponding algorithms are specified by the graphical concurrent programming language of Sleptsov nets. Some significant results are (1) the MR-DBIM is only meaningful when (i.e. sparse scattering domain); (2) the best performance is obtained in the DBIM when Nt = Nr , but in the MR-DBIM when Nr = 2Nt ; (3) the well-investigated value of NN 1 is 2 when and is 3 when .

Noise-Robust Distorted Born Iterative Method with Prior Estimate for Microwave Ablation Monitoring

Noise-Robust Distorted Born Iterative Method with Prior Estimate for Microwave Ablation Monitoring

A Quadratic Programming Approach for Microwave Imaging

Microwave imaging is an emerging technique with applications in various areas, such as geoscience, aviation, and medicine. One of the classic methodologies to address this inverse problem is the Born iterative method (BIM), which divides the nonlinear problem into two linear subproblems: a forward and an inverse one. Several methods can be coupled within this framework to solve the inverse subproblem. This work proposes a formulation for the inverse subproblem in terms of a quadratic programming one, which allows the application of an exact methodology with an adequate mechanism to enforce a particular type of a priori information: the limits of the range of possible contrast values of the objects. This is one of the main contributions of this article and an adaption of the formulation to the use of multiple frequencies and regularization functions. The methodology was able to reconstruct images with few iterations. Several experiments were conducted to evaluate the performance of the proposed methodology in different scenarios considering synthesized geometries and breast phantoms. Mean error per pixel of less than 0.25% for synthesized geometries and 4.6% for breast phantoms (mean value of 0.74% among the experiments) were obtained for the approximations of the scattered field data and the contrast map, in addition to adequately reconstructing objects with different positions, geometries, and contrasts. The comparison between the original BIM and the proposed method with only Tikhonov regularization and no enforcement of prior information showed similar performance. On the other hand, the proposed method with the enforcement of prior information has presented a better performance than the original BIM in 14 of 19 experiments related to the synthesized geometries. The ability to enforce a priori information in the proposed method on the lower and upper bounds of the contrast was responsible for reducing the error by 25%, on average, with respect to the same obtained in the experiments when this information was not considered. In addition, the results also suggested that the enforcement of this information was able to speed up the convergence of the proposed method.