3D microwave tomography with huber regularization applied to realistic numerical breast phantoms

Quantitative active microwave imaging for breast cancer screening and therapy monitoring applications requires adequate reconstruction algorithms, in particular with regard to the nonlinearity and ill-posedness of the inverse problem. We employ a fully vectorial three-dimensional nonlinear inversion algorithm for reconstructing complex permittivity profiles from multi-view single-frequency scattered field data, which is based on a Gauss-Newton optimization of a regularized cost function. We tested it before with various types of regularizing functions for piecewise-constant objects from Institut Fresnel and with a quadratic smoothing function for a realistic numerical breast phantom. In the present paper we adopt a cost function that includes a Huber function in its regularization term, relying on a Markov Random Field approach. The Huber function favors spatial smoothing within homogeneous regions while preserving discontinuities between contrasted tissues. We illustrate the technique with 3D reconstructions from synthetic data at 2GHz for realistic numerical breast phantoms from the University of Wisconsin-Madison UWCEM online repository: we compare Huber regularization with a multiplicative smoothing regularization and show reconstructions for various positions of a tumor, for multiple tumors and for different tumor sizes, from a sparse and from a denser data configuration

Fast Microwave Tomography Algorithm for Breast Cancer Imaging

Microwave tomography has shown promise for breast cancer imaging. The microwaves are harmless to body tissues, which makes microwave tomography a safe adjuvant screening to mammography. Although many clinical studies have shown the effectiveness of regular screening for the detection of breast cancer, the anatomy of the breast and its critical tissues challenge the identification and diagnosis of tumors in this region. Detection of tumors in the breast is more challenging in heterogeneously dense and extremely dense breasts, and microwave tomography has the potential to be effective in such cases. The sensitivity of microwaves to various breast tissues and the comfort and safety of the screening method have made microwave tomography an attractive imaging technique. Despite the need for an alternative screening technique, microwave tomography has not yet been introduced as a screening modality in regular health care, and is still subject to research. The main obstacles are imperfect hardware systems and inefficient imaging algorithms. The immense computational costs for the image reconstruction algorithm present a crucial challenge. 2D imaging algorithms are proposed to reduce the amount of hardware resources required and the imaging time. Although 2D microwave tomography algorithms are computationally less expensive, few imaging groups have been successful in integrating the acquired 3D data into the 2D tomography algorithms for clinical applications. The microwave tomography algorithms include two main computation problems: the forward problem and the inverse problem. The first part of this thesis focuses on a new fast forward solver, the 2D discrete dipole approximation (DDA), which is formulated and modeled. The effect of frequency, sampling number, target size, and contrast on the accuracy of the solver are studied. Additionally, the 2D DDA time efficiency and computation time as a single forward solver are investigated.\ua0 The second part of this thesis focuses on the inverse problem. This portion of the algorithm is based on a log-magnitude and phase transformation optimization problem and is formulated as the Gauss-Newton iterative algorithm. The synthetic data from a finite-element-based solver (COMSOL Multiphysics) and the experimental data acquired from the breast imaging system at Chalmers University of Technology are used to evaluate the DDA-based image reconstruction algorithm. The investigations of modeling and computational complexity show that the 2D DDA is a fast and accurate forward solver that can be embedded in tomography algorithms to produce images in seconds. The successful development and implementation in this thesis of 2D tomographic breast imaging with acceptable accuracy and high computational cost efficiency has provided significant savings in time and in-use memory and is a dramatic improvement over previous implementations

A discrete dipole approximation solver based on the COCG-FFT algorithm and its application to microwave breast imaging

We introduce the discrete dipole approximation (DDA) for efficiently calculating the two-dimensional electric field distribution for our microwave tomographic breast imaging system. For iterative inverse problems such as microwave tomography, the forward field computation is the time limiting step. In this paper, the two-dimensional algorithm is derived and formulated such that the iterative conjugate orthogonal conjugate gradient (COCG) method can be used for efficiently solving the forward problem. We have also optimized the matrix-vector multiplication step by formulating the problem such that the nondiagonal portion of the matrix used to compute the dipole moments is block-Toeplitz. The computation costs for multiplying the block matrices times a vector can be dramatically accelerated by expanding each Toeplitz matrix to a circulant matrix for which the convolution theorem is applied for fast computation utilizing the fast Fourier transform (FFT). The results demonstrate that this formulation is accurate and efficient. In this work, the computation times for the direct solvers, the iterative solver (COCG), and the iterative solver using the fast Fourier transform (COCG-FFT) are compared with the best performance achieved using the iterative solver (COCG-FFT) in C++. Utilizing this formulation provides a computationally efficient building block for developing a low cost and fast breast imaging system to serve under-resourced populations

Design and realisation of a microwave three-dimensional imaging system with application to breast-cancer detection

An active microwave-imaging system for non-invasive detection of breast cancer based on dedicated hardware is described. Thirty-two transceiving channels are used to measure the amplitude and phase of the scattered fields in the three-dimensional (3D) imaging domain using electronic scanning. The 3D inverse electromagnetic scattering problem is then solved in order to reconstruct the distribution of the complex permittivity in the imaging domain. The dedicated hardware is based on an array architecture allowing for a short acquisition time while maintaining a high sensitivity, which is important for measurement accuracy and reproducibility as well as for patient comfort. The dedicated hardware achieves a receiver noise figure of 2.3 dB at a gain of 97 dB. The operating frequency range is from 0.3 to 3 GHz. The image acquisition time at one frequency is approximately 50 s and an image is created within 2 h using the single-frequency reconstruction algorithm. The performance of the system is illustrated by an analysis of the standard deviations in amplitude and phase of a series of measurements as well as by a simple image reconstruction example

Expansion of the nodal-adjoint method for simple and efficient computation of the 2d tomographic imaging jacobian matrix

This paper focuses on the construction of the Jacobian matrix required in tomographic reconstruction algorithms. In microwave tomography, computing the forward solutions during the iterative reconstruction process impacts the accuracy and computational efficiency. Towards this end, we have applied the discrete dipole approximation for the forward solutions with significant time savings. However, while we have discovered that the imaging problem configuration can dramatically impact the computation time required for the forward solver, it can be equally beneficial in constructing the Jacobian matrix calculated in iterative image reconstruction algorithms. Key to this implementation, we propose to use the same simulation grid for both the forward and imaging domain discretizations for the discrete dipole approximation solutions and report in detail the theoretical aspects for this localization. In this way, the computational cost of the nodal adjoint method decreases by several orders of magnitude. Our investigations show that this expansion is a significant enhancement compared to previous implementations and results in a rapid calculation of the Jacobian matrix with a high level of accuracy. The discrete dipole approximation and the newly efficient Jacobian matrices are effectively implemented to produce quantitative images of the simplified breast phantom from the microwave imaging system

Microwave tomography: review of the progress towards clinical applications

Microwave tomography (MWT) is an emerging biomedical imaging modality with great potential for non-invasive assessment of functional and pathological conditions of soft tissues. This paper presents a review of research results obtained by the author and his colleagues and focuses on various potential clinical applications of MWT. Most clinical applications of MWT imaging have complicated, nonlinear, high dielectric contrast inverse problems of three-dimensional diffraction tomography. There is a very high dielectric contrast between bones and fatty areas compared with soft tissues. In most cases, the contrast between soft-tissue abnormalities (the target imaging areas) is less pronounced than between bone (fat) and soft tissue. This additionally complicates the imaging problem. In spite of the difficulties mentioned, it has been demonstrated that MWT is applicable for extremities imaging, breast cancer detection, diagnostics of lung cancer, brain imaging and cardiac imaging

Microwave Antenna System for Muscle Rupture Imaging with a Lossy Gel to Reduce Multipath Interference

Injuries to the hamstring muscles are an increasing problem in sports. Imaging plays a key role in diagnosing and managing athletes with muscle injuries, but there are several problems with conventional imaging modalities with respect to cost and availability. We hypothesized that microwave imaging could provide improved availability and lower costs and lead to improved and more accurate diagnostics. In this paper, a semicircular microwave imaging array with eight antennae was investigated. A key component in this system is the novel antenna design, which is based on a monopole antenna and a lossy gel. The purpose of the gel is to reduce the effects of multipath signals and improve the imaging quality. Several different gels have been manufactured and evaluated in imaging experiments. For comparison, corresponding simulations were performed. The results showed that the gels can effectively reduce the multipath signals and the imaging experiments resulted in significantly more stable and repeatable reconstructions when a lossy gel was used compared to when an almost non-lossy gel was used