3-D Microwave Tomography Using the Soft Prior Regularization Technique: Evaluation in Anatomically Realistic MRI-Derived Numerical Breast Phantoms

On the utilization of the adjoint method in microwave tomography

In microwave imaging, the adjoint method is widely used for the efficient calculation of the update direction, which is then used to update the unknown model parameter. However, the utilization and the formulation of the adjoint method differ significantly depending on the imaging scenario and the applied optimization algorithm. Because of the problem-specific nature of the adjoint formulations, the dissimilarities between the adjoint calculations may be overlooked. Here, we have classified the adjoint method formulations into two groups: the direct and indirect methods. The direct method involves calculating the derivative of the cost function, whereas, in the indirect method, the derivative of the predicted data is calculated. In this review, the direct and indirect adjoint methods are presented, compared, and discussed. The formulations are explicitly derived using the two-dimensional wave equation in frequency and time domains. Finite-difference time-domain simulations are conducted to show the different uses of the adjoint methods for both single source-multiple receiver, and multiple transceiver scenarios. This study demonstrated that an appropriate adjoint method selection is significant to achieve improved computational efficiency for the applied optimization algorithm.

Generation of Prior Information in a Dual-Mode Microwave-Ultrasound Breast Imaging System

A new breast imaging system capable of obtaining ultrasound and microwave scattered-field measurements with minimal or no movement of the breast between measurements has recently been reported. In this work, we describe the methodology that has been developed to generate prior information about the internal structures of the breast based on ultrasound data measured with the dual-mode system. This prior information, estimating both the geometry and complex-valued permittivity of tissues within the breast, is incorporated into the microwave inversion algorithm as a means of enhancing image quality. Several techniques to map reconstructed ultrasound speed to complex-valued relative permittivity are investigated. Quantitative images of two simplified dual-mode breast phantoms obtained using experimental data and the various forms of prior information are presented. Though preliminary, the results presented herein provide an understanding of the impacts of different forms of prior information on dual-mode reconstructions of the breast and can be used to inform future work on the subject.

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 _r and at clinical scenarios compared with conventional DBIM.

Microwave breast tumor localization using wavelet feature extraction and genetic algorithm-neural network

PURPOSE

Ultra-Wide Band (UWB) microwave breast cancer detection is a promising new technology for routine physical examination and home monitoring. The existing microwave imaging algorithms for breast tumor detection are complex and the effect is still not ideal, due to the heterogeneity of breast tissue, skin reflection, and fibroglandular tissue reflection in backscatter signals. This study aims to develop a machine learning method to accurately locate breast tumor.

METHODS

A microwave-based breast tumor localization method is proposed by time-frequency feature extraction and neural network technology. First, the received microwave array signals are converted into representative and compact features by 4-level Discrete Wavelet Transform (DWT) and Principal Component Analysis (PCA). Then, the Genetic Algorithm-Neural Network (GA-NN) is developed to tune hyper-parameters of the neural network adaptively. The neural network embedded in the GA-NN algorithm is a four-layer architecture and 10-fold cross-validation is performed. Through the trained neural network, the tumor localization performance is evaluated on four datasets that are created by FDTD simulation method from 2-D MRI-derived breast models with varying tissue density, shape, and size. Each dataset consists of 1000 backscatter signals with different tumor positions, in which the ratio of training set to test set is 9:1. In order to verify the generalizability and scalability of the proposed method, the tumor localization performance is also tested on a 3-D breast model.

RESULTS

For these 2-D breast models with unknown tumor locations, the evaluation results show that the proposed method has small location errors, which are 0.6076 mm, 3.0813 mm, 2.0798 mm, and 3.2988 mm, respectively, and high accuracy, which is 99%, 80%, 94%, and 85%, respectively. Furthermore, the location error and the prediction accuracy of the 3-D breast model are 3.3896 mm and 81%.

CONCLUSIONS

These evaluation results demonstrate that the proposed machine learning method is effective and accurate for microwave breast tumor localization. The traditional microwave-based breast cancer detection method is to reconstruct the entire breast image to highlight the tumor. Compared with the traditional method, our proposed method can directly get the breast tumor location by applying neural network to the received microwave array signals, and circumvent any complicated image reconstruction processing.

Accurate construction of 3-D numerical breast models with anatomical information through MRI scans

The realistic numerical breast model is an important tool for verifying algorithms, improving design concepts, and exploring new technologies related to microwave breast cancer detection. Recently, several numerical breast models have been developed. However, these models do not include the real breast boundary and the chest region, which causes the electromagnetic wave propagation in the breast models to deviate from the actual situation. The proposed breast models in this paper overcome the significant deficiencies of the recent breast models in terms of structure completeness and authenticity. The model construction based on magnetic resonance imaging (MRI) scans is a multistep approach. Firstly, intensity inhomogeneity in MRI images is corrected by an improved nonparametric nonuniform intensity normalization (N4) algorithm. Then, a dual threshold and morphological transformation (DTMT) method is developed to segment the real breast region. Subsequently, a modified maximum inter-class variance (MICV) method is employed to automatically divide the breast region into the fat and the fibroglandular clusters with desired complexity. Finally, the dielectric properties of breast tissues are calculated by a piecewise weighted mapping method. The applicability and effectiveness of the proposed method are verified by constructing four breast models with varying tissue density, shape, and size. The constructed models in this study are significant to achieve reliable and precise effects for microwave breast cancer detection due to the accurate expression of the breast anatomical information and electromagnetic characteristics.

Full 3D Microwave Breast Imaging Using a Deep-Learning Technique

A deep learning technique to enhance 3D images of the complex-valued permittivity of the breast obtained via microwave imaging is investigated. The developed technique is an extension of one created to enhance 2D images. We employ a 3D Convolutional Neural Network, based on the U-Net architecture, that takes in 3D images obtained using the Contrast-Source Inversion (CSI) method and attempts to produce the true 3D image of the permittivity. The training set consists of 3D CSI images, along with the true numerical phantom images from which the microwave scattered field utilized to create the CSI reconstructions was synthetically generated. Each numerical phantom varies with respect to the size, number, and location of tumors within the fibroglandular region. The reconstructed permittivity images produced by the proposed 3D U-Net show that the network is not only able to remove the artifacts that are typical of CSI reconstructions, but it also enhances the detectability of the tumors. We test the trained U-Net with 3D images obtained from experimentally collected microwave data as well as with images obtained synthetically. Significantly, the results illustrate that although the network was trained using only images obtained from synthetic data, it performed well with images obtained from both synthetic and experimental data. Quantitative evaluations are reported using Receiver Operating Characteristics (ROC) curves for the tumor detectability and RMS error for the enhancement of the reconstructions.

On the Orbital Angular Momentum Incident Fields in Linearized Microwave Imaging

Orbital angular momentum (OAM) is gaining great attention in the physics and electromagnetic community owing to an intriguing debate concerning its suitability for widening channel capacity in next-generation wireless communications. While such a debate is still a matter of controversy, we exploit OAM generation for microwave imaging within the classical first order linearized models, i.e., Born and Rytov approximation. Physical insights into different fields carrying ℓ-order OAM are conveniently exploited to propose possible alternative imaging approaches and paradigms in microwave imaging.