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RF Breast Cancer Detection Employing a Noncharacterized Vivaldi Antenna and a MUSIC-Inspired Algorithm
Abstract and Figures
A novel microwave breast cancer detection system consisting of an Evolutionary Global Optimized Vivaldi antenna and an algorithm inspired by MUltiple SIgnal Classification (MUSIC) is presented. Its performance is assessed by using a simplified numerical breast phantom for a number of critical conditions including the presence of fibroglandular tissues.
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... However, the LSM requires a large number of directions of the incident and corresponding scattered fields, and most of the research deals with the full-view inverse scattering problem. MUltiple SIgnal Classification (MUSIC), which is a method of characterizing the range of a self-adjoint operator (see [26] for instance), is also applied to various inverse scattering problems and microwave imaging [27][28][29]. Let us mention that the location of small scatterers can be identified clearly through the MUSIC in the full-view problem, but, in the limited-view problem, incorrect locations are retrieved, refer to [30]. ...
Generally, the results of imaging the limited view data in the inverse scattering problem are relatively poor, compared to those of imaging the full view data. It is known that solving this problem mathematically is very difficult. Therefore, the main purpose of this study is to solve the inverse scattering problem in the limited view situation for some cases by using artificial intelligence. Thus, we attempted to develop an artificial intelligence suitable for problem-solving for the cases where the number of scatterers was 2 and 3, respectively, based on CNN (Convolutional Neural Networks) and ANN (Artificial Neural Network) models. As a result, when the ReLU function was used as the activation function and ANN consisted of four hidden layers, a learning model with a small mean square error of the output data through the ground truth data and this learning model could be developed. In order to verify the performance and overfitting of the developed learning model, limited view data that were not used for learning were newly created. The mean square error between output data obtained from this and ground truth data was also small, and the data distributions between the two data were similar. In addition, the locations of scatterers by imaging the out data with the subspace migration algorithm could be accurately found. To support this, data related to artificial neural network learning and imaging results using the subspace migration algorithm are attached.
... Alternatively, various non-iterative schemes have been designed and successfully applied to MI, such as multiple signal classification (MUSIC) [20,21], migration techniques [22,23], direct and orthogonality sampling methods [24,25], and the factorization method [3,26]. Most of these techniques are developed under the multistatic measurement system (MMS). ...
We develop a sampling-type algorithm for localizing a small object from scattering parameter data measured in a bistatic configuration. To this end, we design a sampling-type imaging function based on the integral equation formula for the scattering parameter. To clarify its applicability, we show that the imaging function can be expressed by the bistatic angle, antenna arrangement, and Bessel function of an integer order. This result reveals some properties of the imaging function and influence of the selection of the bistatic angle. Numerical experiments are carried out for single and multiple small and large objectives to illustrate the pros and cons of the developed algorithm.
... Most inversion operators are in a form of weighted adjoint of the scattering operator. Indeed, they attempt to achieve focusing in the scatterer region by compensating the phase term and possibly equalizing the amplitude term [31]- [33]. Here, we just consider the actual adjoint, A † , of the scattering operator, that is ...
In this paper, the problem of how to spatially sample the scattered field in microwave through-the wall imaging is addressed.
To this end, a two-dimensional scalar configuration for a three-layered back-ground medium is considered under a linearized
scattering model. The aim is to collect as low as possible measurements by maintaining the same performance in the reconstructions.
Accordingly, the number and the positions of the spatial measurement points are determined so that the point-spread function of
the resulting semi-discrete problem approximates well the one of the ideal continuous case (i.e., when data space is not sampled at
all). It is shown that the resulting measurement spatial positions must be non-uniformly arranged across the measurement domain
and their number is generally much lower than the one returned by some literature sampling criteria. Also, the measurement points
can be analytically determined by taking into account the geometrical parameters as well as the wall features. Numerical examples
are included to check the theoretical arguments.
... Most inversion operators are in a form of weighted adjoint of the scattering operator. Indeed, they attempt to achieve focusing in the scatterer region by compensating the phase term and possibly equalizing the amplitude term [31] - [33]. Here, we just consider the actual adjoint, A † , of the scattering operator, that is ...
In this paper, the problem of how to spatially sample the scattered field in microwave through-the wall imaging is addressed. To this end, a two-dimensional scalar configuration for a three-layered background medium is considered under a linearized scattering model. The aim is to collect as low as possible measurements by maintaining the same performance in the reconstructions. Accordingly, the number and the positions of the spatial measurement points are determined so that the point-spread function of the resulting semi-discrete problem approximates well the one of the ideal continuous case (i.e., when data space is not sampled at all). It is shown that the resulting measurement spatial positions must be non-uniformly arranged across the measurement domain and their number is generally much lower than the one returned by some literature sampling criteria. Also, the measurement points can be analytically determined by taking into account the geometrical parameters as well as the wall features. Numerical examples are included to check the theoretical arguments.
... Therefore, the achievable performance is negatively affected by frequency dispersion of breast tissues (which are unknown or known with a considerable degree of uncertainty and vary from patient to patient) as well as by the antenna frequency response, which is hard to predict because it is in close proximity to breast. As shown in [30,31], this drawback can be mitigated by employing non-coherent imaging strategies. In particular in those papers we introduced and compared incoherent versions of beam-forming and MUSIC [32] (I-MUSIC) and showed that the performance remains stable by using different types of antennas although they were non-characterized, i.e., their frequency responses were not estimated nor enclosed in the model upon which the algorithms were based. ...
In this study, we investigate MUltiple SIgnal Classification (MUSIC) operated at a fixed frequency for identifying the locations of short, linear perfectly conducting cracks in limited-aperture inverse scattering problem. At present, the so-called multi-static response (MSR) matrix whose elements are measured far-field pattern data is neither symmetric nor Hermitian, a projection operator onto the noise subspace cannot be defined using the conventional method, so the imaging function cannot be designed. Motivated by this fact, we first propose a novel MUSIC imaging function in limited-aperture inverse scattering problem. This is based on the asymptotic expansion formula for far-field patterns in the presence of small cracks and the structure of singular vectors associated with nonzero singular values of the MSR matrix. Next, the new imaging function was analyzed by establishing a relationship with an infinite series of the Bessel function of the integer order of the first kind and ranges of incident and observation directions. We then observe some properties of MUSIC in limited-aperture problems and show that the proposed imaging function is a generalization of full- and limited-view problems. We finally validate the feasibility and limitation of the proposed MUSIC imaging function through numerical simulation results using synthetic and real data.
We apply MUltiple SIgnal Classification (MUSIC) algorithm for the location reconstruction of a set of two-dimensional circle-like small inhomogeneities in the limited-aperture inverse scattering problem. Compared with the full- or limited-view inverse scattering problem, the collected multi-static response (MSR) matrix is no more symmetric (thus not Hermitian), and therefore, it is difficult to define the projection operator onto the noise subspace through the traditional approach. With the help of an asymptotic expansion formula in the presence of small inhomogeneities and the structure of the MSR-matrix singular vector associated with nonzero singular values, we define an alternative projection operator onto the noise subspace and the corresponding MUSIC imaging function. To demonstrate the feasibility of the designed MUSIC, we show that the imaging function can be expressed by an infinite series of integer-order Bessel functions of the first kind and the range of incident and observation directions. Furthermore, we identify that the main factors of the imaging function for the permittivity and permeability contrast cases are the Bessel function of order zero and one, respectively. This further implies that the imaging performance significantly depends on the range of incident and observation directions; peaks of large magnitudes appear at the location of inhomogeneities for permittivity contrast case, and for the permeability contrast case, peaks of large magnitudes appear at the location of inhomogeneities when the range of such directions are narrow, while two peaks of large magnitudes appear in the neighborhood of the location of inhomogeneities when the range is wide enough. The numerical simulation results via noise-corrupted synthetic data also show that the designed MUSIC algorithm can address both permittivity and permeability contrast cases.
This study concerns a subspace migration technique used to identify the shape and location of an unknown anomaly from scattered parameter data collected within the scattering matrix for a limited-aperture inverse scattering problem. The mathematical theories of subspace migration are partially understood in terms of limited-aperture inverse scattering problems, but little investigation of real-world applications, such as microwave imaging, has taken place. Hence, we perform further research to analyze the subspace migration and explain the reasons for a number of unexplained phenomena. For theoretical corroboration, we prove that the imaging function of subspace migration is composed of an infinite series of integer-order Bessel functions of the first kind, and we outline the arrangement and the total number of antennas for transmitting and receiving signals. This is based on the application of the Born approximation to the identification of an anomaly and the uniform convergence of the Jacobi–Anger expansion formula. Various results of numerical simulations with synthetic and real data are exhibited to support the theoretical results of the imaging function and explain the reasons for a number of phenomena as well as the fundamental limitations. Further, we suggest a method of antenna arrangement to obtain better results and confirm the improvements through simulations.
This paper presents a novel stochastic microwave method for the detection, location and reconstruction of electric properties of breast cancer in a simplified breast phantom. The method is based on the inversion of time domain data. The problem is recast as an optimization one by defining a suitable cost function which is then minimized using an efficient evolutionary algorithm. Selected numerical simulations of a simplified three dimensional breast model and a realistic numerical phantom based on magnetic resonance images (MRIs) are carried out to assess the capabilities of the method. The results obtained show that the proposed method is able to reconstruct the properties of a tumor-like inclusion to a reasonable degree of accuracy.
Ultra wideband (UWB) Microwave imaging is one of the most promising emerging imaging technologies for breast cancer detection, and is based on the dielectric contrast between normal and cancerous tissues at microwave frequencies. UWB radar imaging involves illuminating the breast with a microwave pulse and reflected signals are used to determine the presence and location of significant dielectric scatterers, which may be representative of cancerous tissue within the breast. Beamformers are used to spatially focus the reflected signals and to compensate for path dependent attenuation and phase effects. While these beamforming algorithms have often been evaluated in isolation, variations in experimental conditions and metrics prompts the assessment of the beamformers on common anatomically and dielectrically representative breast models in order to effectively compare the performance of each. This paper seeks to investigate the following beamforming algorithms: Monostatic and Multistatic Delay-And-Sum (DAS), Delay-Multiply-And-Sum (DMAS) and Improved Delay-And-Sum (IDAS). The performance of each beamformer is evaluated across a range of appropriate metrics.
Ultra Wideband (UWB) radar has been extensively investigated as a means of detecting early-stage breast cancer. The basis for this imaging modality is the dielectric contrast between normal and cancerous breast tissue at microwave frequencies. However, based on the dielectric similarities between a malignant and a benign tumour within the breast, differentiating between these types of tissues in microwave images may be problematic. Therefore, it is important to investigate alternative methods to analyse and classify dielectric scatterers within the breast, taking into account other tumour characteristics such as shape and surface texture of tumours. Benign tumours tend to have smooth surfaces and oval shapes whereas malignant tumours tend to have rough and complex surfaces with spicules or microlobules. Consequently, one classification approach is to classify scatterers based on their Radar Target Signature (RTS), which carries important information about scatterer size and shape. In this paper, Gaussian Random Spheres (GRS) are used to model the shape and size of benign and malignant tumours. Principal Components Analysis (PCA) is used to extract information from the RTS of the tumours, while eight different combinations of tumour classifiers are analysed in terms of performance and are compared in terms of two possible approaches: Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA).
A planar antenna array that includes 12 corrugated tapered slot elements for use in ultrawideband (UWB) biomedical microwave imaging systems is presented. The used corrugate tapered slot antenna has a compact size, low profile, moderate gain, and distortionless performance in the time domain. The array is immersed in a carefully designed matching liquid of suitable dielectric constant to improve the matching between the array and the imaged object, and thus, to increase the dynamic range of the imaging system. A suitable platform is designed and fabricated to accommodate the array, breast phantom, and a coupling liquid for the case of UWB breast imaging. The design of the whole system is optimized using trust-region framework method in the simulation tool CST Microwave Studio. The performance of the designed array is confirmed via measurements in a realistic imaging environment. © 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2013. © 2013 Wiley Periodicals, Inc.
Microwaves and millimeter waves have been used extensively to image dielectric bodies. The application of microwaves in biomedical imaging and diagnostics, however, remains a field with many uncharted territories. This article is an overview on medical imaging using microwave imaging for breast cancer and its challenges, hopes, and outlook.
Microwave imaging is a pervasive research field andis useful in numerous applicative diagnostic noninvasive contexts. This paper focuses on two aspects. First, we perform a numerical investigation to assess the role played by fundamental parameters (i.e. number of sensors, operating frequency bandwidth) on cancer detection. To this end, a simplified cylindrical phantom probed by ideal two-dimensional dipoles (i.e. infinitely long along the axis of invariance) is considered. Second, in order to focus on the role of the antennas, we analyze, still by numerical simulations and for a simplified breast model, how performances vary when a realistic antenna is adopted.