Variational Bayesian inversion for microwave breast imaging

International audienceMicrowave imaging is considered as a nonlinear inverse scattering problem and tackled in a Bayesian estimation framework. The object under test (a breast affected by a tumor) is assumed to be composed of compact regions made of a restricted number of different homogeneous materials. This a priori knowledge is defined by a Gauss-Markov-Potts distribution. First, we express the joint posterior of all the unknowns; then, we present in detail the variational Bayesian approximation used to compute the estimators and reconstruct both permittivity and conductivity maps. This approximation consists of the best separable probability law that approximates the true posterior distribution in the Kullback-Leibler sense. This leads to an implicit parametric optimization scheme which is solved iteratively. Some preliminary results, obtained by applying the proposed method to synthetic data, are presented and compared with those obtained by means of the classical contrast source inversion method

Variational Bayesian inversion for microwave breast imaging

International audienceMicrowave imaging is considered as a nonlinear inverse scattering problem and tackled in a Bayesian estimation framework. The object under test (a breast affected by a tumor) is assumed to be composed of compact regions made of a restricted number of different homogeneous materials. This a priori knowledge is defined by a Gauss-Markov-Potts distribution. First, we express the joint posterior of all the unknowns; then, we present in detail the variational Bayesian approximation used to compute the estimators and reconstruct both permittivity and conductivity maps. This approximation consists of the best separable probability law that approximates the true posterior distribution in the Kullback-Leibler sense. This leads to an implicit parametric optimization scheme which is solved iteratively. Some preliminary results, obtained by applying the proposed method to synthetic data, are presented and compared with those obtained by means of the classical contrast source inversion method

Application-Specific Broadband Antennas for Microwave Medical Imaging

The goal of this work is the introduction of efficient antenna structures on the basis of the requirement of different microwave imaging methods; i.e. quantitative and qualitative microwave imaging techniques. Several criteria are proposed for the evaluation of single element antenna structures for application in microwave imaging systems. The performance of the proposed antennas are evaluated in simulation and measurement scenarios

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

On the 3D electromagnetic quantitative inverse scattering problem: algorithms and regularization

In this thesis, 3D quantitative microwave imaging algorithms are developed with emphasis on efficiency of the algorithms and quality of the reconstruction. First, a fast simulation tool has been implemented which makes use of a volume integral equation (VIE) to solve the forward scattering problem. The solution of the resulting linear system is done iteratively. To do this efficiently, two strategies are combined. First, the matrix-vector multiplications needed in every step of the iterative solution are accelerated using a combination of the Fast Fourier Transform (FFT) method and the Multilevel Fast Multipole Algorithm (MLFMA). It is shown that this hybridMLFMA-FFT method is most suited for large, sparse scattering problems. Secondly, the number of iterations is reduced by using an extrapolation technique to determine suitable initial guesses, which are already close to the solution. This technique combines a marching-on-in-source-position scheme with a linear extrapolation over the permittivity under the form of a Born approximation. It is shown that this forward simulator indeed exhibits a better efficiency. The fast forward simulator is incorporated in an optimization technique which minimizes the discrepancy between measured data and simulated data by adjusting the permittivity profile. A Gauss-Newton optimization method with line search is employed in this dissertation to minimize a least squares data fit cost function with additional regularization. Two different regularization methods were developed in this research. The first regularization method penalizes strong fluctuations in the permittivity by imposing a smoothing constraint, which is a widely used approach in inverse scattering. However, in this thesis, this constraint is incorporated in a multiplicative way instead of in the usual additive way, i.e. its weight in the cost function is reduced with an improving data fit. The second regularization method is Value Picking regularization, which is a new method proposed in this dissertation. This regularization is designed to reconstruct piecewise homogeneous permittivity profiles. Such profiles are hard to reconstruct since sharp interfaces between different permittivity regions have to be preserved, while other strong fluctuations need to be suppressed. Instead of operating on the spatial distribution of the permittivity, as certain existing methods for edge preservation do, it imposes the restriction that only a few different permittivity values should appear in the reconstruction. The permittivity values just mentioned do not have to be known in advance, however, and their number is also updated in a stepwise relaxed VP (SRVP) regularization scheme. Both regularization techniques have been incorporated in the Gauss-Newton optimization framework and yield significantly improved reconstruction quality. The efficiency of the minimization algorithm can also be improved. In every step of the iterative optimization, a linear Gauss-Newton update system has to be solved. This typically is a large system and therefore is solved iteratively. However, these systems are ill-conditioned as a result of the ill-posedness of the inverse scattering problem. Fortunately, the aforementioned regularization techniques allow for the use of a subspace preconditioned LSQR method to solve these systems efficiently, as is shown in this thesis. Finally, the incorporation of constraints on the permittivity through a modified line search path, helps to keep the forward problem well-posed and thus the number of forward iterations low. Another contribution of this thesis is the proposal of a new Consistency Inversion (CI) algorithm. It is based on the same principles as another well known reconstruction algorithm, the Contrast Source Inversion (CSI) method, which considers the contrast currents – equivalent currents that generate a field identical to the scattered field – as fundamental unknowns together with the permittivity. In the CI method, however, the permittivity variables are eliminated from the optimization and are only reconstructed in a final step. This avoids alternating updates of permittivity and contrast currents, which may result in a faster convergence. The CI method has also been supplemented with VP regularization, yielding the VPCI method. The quantitative electromagnetic imaging methods developed in this work have been validated on both synthetic and measured data, for both homogeneous and inhomogeneous objects and yield a high reconstruction quality in all these cases. The successful, completely blind reconstruction of an unknown target from measured data, provided by the Institut Fresnel in Marseille, France, demonstrates at once the validity of the forward scattering code, the performance of the reconstruction algorithm and the quality of the measurements. The reconstruction of a numerical MRI based breast phantom is encouraging for the further development of biomedical microwave imaging and of microwave breast cancer screening in particular

Microwave Sensing and Imaging

In recent years, microwave sensing and imaging have acquired an ever-growing importance in several applicative fields, such as non-destructive evaluations in industry and civil engineering, subsurface prospection, security, and biomedical imaging. Indeed, microwave techniques allow, in principle, for information to be obtained directly regarding the physical parameters of the inspected targets (dielectric properties, shape, etc.) by using safe electromagnetic radiations and cost-effective systems. Consequently, a great deal of research activity has recently been devoted to the development of efficient/reliable measurement systems, which are effective data processing algorithms that can be used to solve the underlying electromagnetic inverse scattering problem, and efficient forward solvers to model electromagnetic interactions. Within this framework, this Special Issue aims to provide some insights into recent microwave sensing and imaging systems and techniques

Simulation and Design of an UWB Imaging System for Breast Cancer Detection

Breast cancer is the most frequently diagnosed cancer among women. In recent years, the mortality rate due to this disease is greatly decreased thanks to both enormous progress in cancer research, and screening campaigns which have allowed the increase in the number of early diagnoses of the disease. In fact, if the tumor is identied in its early stage, e.g. when it has a diameter of less than one centimeter, the possibility of a cure can reach 93%. However, statistics show that more young aged women are suered breast cancer. The goal of screening exams for early breast cancer detection is to nd cancers before they start to cause symptoms. Regular mass screening of all women at risk is a good option to achieve that. Instead of meeting very high diagnostic standards, it is expected to yield an early warning, not a denitive diagnosis. In the last decades, X-ray mammography is the most ecient screening technique. However, it uses ionizing radiation and, therefore, should not be used for frequent check-ups. Besides, it requires signicant breast compression, which is often painful. In this scenario many alternative technologies were developed to overcome the limitations of mammography. Among these possibilities, Magnetic Resonance Imaging (MRI) is too expensive and time-consuming, Ultrasound is considered to be too operatordependent and low specicity, which are not suitable for mass screening. Microwave imaging techniques, especially Ultra WideBand (UWB) radar imaging, is the most interesting one. The reason of this interest relies on the fact that microwaves are non-ionizing thus permitting frequent examinations. Moreover, it is potentially lowcost and more ecient for young women. Since it has been demonstrated in the literatures that the dielectric constants between cancerous and healthy tissues are quite dierent, the technique consists in illuminating these biological tissues with microwave radiations by one or more antennas and analyzing the re ected signals. An UWB imaging system consists of transmitters, receivers and antennas for the RF part, the transmission channel and of a digital backend imaging unit for processing the received signals. When an UWB pulse strikes the breast, the pulse is re ected due to the dielectric discontinuity in tissues, the bigger the dierence, the bigger the backscatter. The re ected signals are acquired and processed to create the energy maps. This thesis aims to develop an UWB system at high resolution for the detection of carcinoma breast already in its initial phase. To favor the adoption of this method in screening campaigns, it is necessary to replace the expensive and bulky RF instrumentation used so far with ad-hoc designed circuits and systems. In order to realize that, at the very beginning, the overall system environment must be built and veried, which mainly consists of the transmission channel{the breast model and the imaging unit. The used transmission channel data come from MRI of the prone patient. In order to correctly use this numerical model, a simulator was built, which was implemented in Matlab, according to the Finite-Dierence-Time- Domain (FDTD) method. FDTD algorithm solves the electric and magnetic eld both in time and in space, thus, simulates the propagation of electromagnetic waves in the breast model. To better understand the eect of the system non-idealities, two 2D breast models are investigated, one is homogeneous, the other is heterogeneous. Moreover, the modeling takes into account all critical aspects, including stability and medium dispersion. Given the types of tissues under examination, the frequency dependence of tissue dielectric properties is incorporated into wideband FDTD simulations using Debye dispersion parameters. A performed further study is in the implementation of the boundary conditions. The Convolution Perfectly Matched Layer (CPML) is used to implement the absorbing boundaries. The objective of the imaging unit is to obtain an energy map representing the amount of energy re ected from each point of the breast, by recombining the sampled backscattered signals. For this purpose, the study has been carried out on various beamforming in the literature. The basic idea is called as "delay and sum", which is to align the received signals in such a way as to focus a given point in space and then add up all the contributions, so as to obtain a constructive interference at that point if this is a diseased tissue. In this work, Microwave Imaging via Space Time (MIST) Beamforming algorithm is applied, which is based on the above principle and add more elaborations of the signals in order to make the algorithm less sensitive to propagation phenomena in the medium and to the non-idealities of the system. It is divided into two distinct steps: the rst step, called SKin Artifact Removal (SKAR), takes care of removing the contributions from the signal caused by the direct path between the transmitter and receiver, the re ection of skin, as they are orders of magnitude higher compared to the re ections caused by cancers; the second step, which is BEAmForming (BEAF), performs the algorithm of reconstruction by forming a weighted combination of time delayed version of the calibrated re ected signals. As discussed above, more attention must be paid on the implementation of the ad-hoc integration circuits. In this scenario, due to the strict requirements on the RF receiver component, two dierent approaches of the implementation of the RF front-end, Direct Conversion (DC) receiver and Coherent Equivalent Time Sampling (CETS) receiver are compared. They are modeled behaviorally and the eects of various impairments, such as thermal, jitter, and phase noise, as well as phase inaccuracies, non-linearity, ADC quantization noise and distortion, on energy maps and on quantitative metrics such as SCR and SMR are evaluated. Dierential Gaussian pulse is chosen as the exciting source. Results show that DC receiver performs higher sensitivity to phase inaccuracies, which makes it less robust than the CETS receiver. Another advantage of the CETS receiver is that it can work in time domain with UWB pulses, other than in frequency domain with stepped frequency continuous waves like the DC one, which reduces the acquisition time without impacting the performance. Based on the results of the behavioral simulations, low noise amplier (LNA) and Track and Hold Amplier (THA) can be regarded as the most critical parts for the proposed CETS receiver, as well as the UWB antenna. This work therefore focuses on their hardware implementations. The LNA, which shows critical performance limitation at bandwidth and noise gure of receiver, has been developed based on common-gate conguration. And the THA based on Switched Source Follower (SSF) scheme has been presented and improved to obtain high input bandwidth, high sampling rate, high linearity and low power consumption. LNA and THA are implemented in CMOS 130nm technology and the circuit performance evaluation has been taken place separately and together. The small size UWB wide-slot antenna is designed and simulated in HFSS. Finally, in order to evaluate the eect of the implemented transistor level components on system performance, a multi-resolution top-down system methodology is applied. Therfore, the entire ow is analyzed for dierent levels of the RF frontend. Initially the system components are described behaviorally as ideal elements. The main activity consists in the analysis and development of the entire frontend system, observing and complementing each other blocks in a single ow simulation, clear and well-dened in its various interfaces. To achieve that the receiver is modeled and analyzed using VHDL-AMS language block by block, moreover, the impact of quantization, noise, jitter, and non-linearity is also evaluated. At last, the behavioral description of antenna, LNA and THA is replaced with a circuit-level one without changing the rest of the system, which permits a system-level assessment of low-level issues

Advanced Computational Methods for Oncological Image Analysis

[Cancer is the second most common cause of death worldwide and encompasses highly variable clinical and biological scenarios. Some of the current clinical challenges are (i) early diagnosis of the disease and (ii) precision medicine, which allows for treatments targeted to specific clinical cases. The ultimate goal is to optimize the clinical workflow by combining accurate diagnosis with the most suitable therapies. Toward this, large-scale machine learning research can define associations among clinical, imaging, and multi-omics studies, making it possible to provide reliable diagnostic and prognostic biomarkers for precision oncology. Such reliable computer-assisted methods (i.e., artificial intelligence) together with clinicians’ unique knowledge can be used to properly handle typical issues in evaluation/quantification procedures (i.e., operator dependence and time-consuming tasks). These technical advances can significantly improve result repeatability in disease diagnosis and guide toward appropriate cancer care. Indeed, the need to apply machine learning and computational intelligence techniques has steadily increased to effectively perform image processing operations—such as segmentation, co-registration, classification, and dimensionality reduction—and multi-omics data integration.