Three Dimensional Microwave Data Inversion in Feature Space for Stroke Imaging.

Microwave imaging is a promising method for early diagnosing and monitoring brain strokes. It is portable, non-invasive, and safe to the human body. Conventional techniques solve for unknown electrical properties represented as pixels or voxels, but often result in inadequate structural information and high computational costs. We propose to reconstruct the three dimensional (3D) electrical properties of the human brain in a feature space, where the unknowns are latent codes of a variational autoencoder (VAE). The decoder of the VAE, with prior knowledge of the brain, acts as a module of data inversion. The codes in the feature space are optimized by minimizing the misfit between measured and simulated data. A dataset of 3D heads characterized by permittivity and conductivity is constructed to train the VAE. Numerical examples show that our method increases structural similarity by 14% and speeds up the solution process by over 3 orders of magnitude using only 4.8% number of the unknowns compared to the voxel-based method. This high-resolution imaging of electrical properties leads to more accurate stroke diagnosis and offers new insights into the study of the human brain.

Deep feature-domain matching for cardiac-related component separation from a chest electrical impedance tomography image series: proof-of-concept study.

Objectives.The cardiac-related component in chest electrical impedance tomography (EIT) measurement is of potential value to pulmonary perfusion monitoring and cardiac function measurement. In a spontaneous breathing case, cardiac-related signals experience serious interference from ventilation-related signals. Traditional cardiac-related signal-separation methods are usually based on certain features of signals. To further improve the separation accuracy, more comprehensive features of the signals should be exploited.Approach.We propose an unsupervised deep-learning method called deep feature-domain matching (DFDM), which exploits the feature-domain similarity of the desired signals and the breath-holding signals. This method is characterized by two sub-steps. In the first step, a novel Siamese network is designed and trained to learn common features of breath-holding signals; in the second step, the Siamese network is used as a feature-matching constraint between the separated signals and the breath-holding signals.Main results.The method is first tested using synthetic data, and the results show satisfactory separation accuracy. The method is then tested using the data of three patients with pulmonary embolism, and the consistency between the separated images and the radionuclide perfusion scanning images is checked qualitatively.Significance.The method uses a lightweight convolutional neural network for fast network training and inference. It is a potential method for dynamic cardiac-related signal separation in clinical settings.

Supervised Descent Learning for Thoracic Electrical Impedance Tomography.

OBJECTIVE: The absolute image reconstruction problem of electrical impedance tomography (EIT) is ill-posed. Traditional methods usually solve a nonlinear least squares problem with some kind of regularization. These methods suffer from low accuracy, poor anti-noise performance, and long computation time. Besides, the integration of a priori information is not very flexible. This work tries to solve EIT inverse problem using a machine learning algorithm for the application of thorax imaging. METHODS: We developed the supervised descent learning EIT (SDL-EIT) inversion algorithm based on the idea of supervised descent method (SDM). The algorithm approximates the mapping from measured data to the conductivity image by a series of descent directions learned from training samples. We designed a training data set in which the thorax contour, and some general structure of lungs, and heart are embedded. The algorithm is implemented in both two-, and three-dimensional cases, and is evaluated using synthetic, and measured thoracic data. Results, and conclusion: For synthetic data, SDL-EIT shows better accuracy, and anti-noise performance compared with traditional Gauss-Newton inversion (GNI) method. For measured data, the result of SDL-EIT is reasonable compared with computed tomography (CT) scan image. SIGNIFICANCE: Using SDL-EIT, prior information can be easily integrated through the specifically designed training data set, and the image reconstruction process can be accelerated. The algorithm is effective in inverting measured thoracic data. It is a potential algorithm for human thorax imaging.

Neural network-based supervised descent method for 2D electrical impedance tomography.

OBJECTIVE: In this work, we study the application of the neural network-based supervised descent method (NN-SDM) for 2D electrical impedance tomography. APPROACH: The NN-SDM contains two stages: offline training and online prediction. In the offline stage, neural networks are iteratively applied to learn a sequence of descent directions for minimizing the objective function, where the training data set is generated in advance according to prior information or historical data. In the online stage, the trained neural networks are directly used to predict the descent directions. MAIN RESULTS: Numerical and experimental results are reported to assess the efficiency and accuracy of the NN-SDM for both model-based and pixel-based inversions. In addition, the performance of the NN-SDM is compared with the linear SDM (LSDM), an end-to-end neural network (E2E-NN) and the Gauss-Newton (GN) method. The results demonstrate that the NN-SDM achieves faster convergence than the LSDM and GN method, and achieves a stronger generalization ability than the E2E-NN. SIGNIFICANCE: The NN-SDM combines the strong non-linear fitting ability of the neural network and good generalization capability of the supervised descent method (SDM), which also provides good flexibility to incorporate prior information and accelerates the convergence of iteration.

Study on 3-D Acoustic Imaging for Human Thorax Based on Contrast Source Inversion.

In this article, we study a 3-D acoustic imaging algorithm that can reconstruct compressibility, attenuation, and density simultaneously based on the contrast source inversion (CSI) method. This is a nonlinear and ill-posed inverse problem. To deal with the nonlinearity, we introduce two asymmetrical contrast sources that are functions of the contrasts and the total field. In this case, the scattered field and the total field are linear with the two contrast sources, and the two contrast sources are also linear with the two contrasts; thus, the nonlinearity is partially alleviated. To mitigate the ill-posedness of this inverse problem, we apply a multifrequency, multitransmitter, and multireceiver setting. Besides, to ensure the robustness of the algorithm, two multiplicative regularization terms are introduced as additional constraints. The reconstruction of those acoustic parameters can be achieved by alternately updating the contrast sources and the contrasts from the knowledge of the pressure field. Numerical studies show good reconstruction of compressibility, attenuation, and density of the synthetic thorax model, which validates the feasibility of imaging human thorax using low-frequency ultrasound.

Three-Dimensional Electrical Impedance Tomography With Multiplicative Regularization.

OBJECTIVE: The multiplicative regularization scheme is applied to three-dimensional electrical impedance tomography (EIT) image reconstruction problem to alleviate its ill-posedness. METHODS: A cost functional is constructed by multiplying the data misfit functional with the regularization functional. The regularization functional is based on a weighted L2-norm with the edge-preserving characteristic. Gauss-Newton method is used to minimize the cost functional. A method based on the discrete exterior calculus (DEC) theory is introduced to formulate the discrete gradient and divergence operators related to the regularization on unstructured meshes. RESULTS: Both numerical and experimental results show good reconstruction accuracy and anti-noise performance of the algorithm. The reconstruction results using human thoracic data show promising applications in thorax imaging. CONCLUSION: The multiplicative regularization can be applied to EIT image reconstruction with promising applications in thorax imaging. SIGNIFICANCE: In the multiplicative regularization scheme, there is no need to set an artificial regularization parameter in the cost functional. This helps to reduce the workload related to choosing a regularization parameter which may require expertise and many numerical experiments. The DEC-based method provides a systematic and rigorous way to formulate operators on unstructured meshes. This may help EIT image reconstructions using regularizations imposing structural or spatial constraints.

Feasibility study of acoustic imaging for human thorax using an acoustic contrast source inversion algorithm.

In this work, an acoustic imaging method based on contrast source inversion and its feasibility in quantitatively reconstructing compressibility, attenuation, and density of human thorax is studied. In the acoustic wave equation, the inhomogeneity in density makes the relationship between the contrasts and the total pressure highly nonlinear. To reduce this nonlinearity, two contrast sources are introduced to ensure symmetry in the equation, such that the inverse problem can be solved efficiently by alternately updating two contrast sources and two contrasts. Moreover, to improve the stability of the algorithm, the multiplicative regularization scheme with two additive regularization factors is applied. Using this algorithm, acoustic parameters of human thorax from low frequency ultrasound measurement are reconstructed. Numerical results show that the acoustic parameters of human thorax can be properly reconstructed at frequency of tens of kHz using this algorithm.

The contrast-source stress-velocity integral-equation formulation of three-dimensional time-domain elastodynamic scattering problems: a structured approach using tensor partitioning.

The contrast-source stress-velocity integral-equation formulation of three-dimensional time-domain elastodynamic scattering problems is discussed. A novel feature of the formulation is a tensor partitioning of the relevant dynamic stress and the contrast source volume density of deformation rate. The partitioning highlights several features about the structure of the formulation. These can advantageously be incorporated in a computational implementation of the method. An application to the case of a scatterer composed of isotropic material and embedded in an isotropic elastic background medium shows that the corresponding newly introduced constitutive coefficients are more natural as a characterization of the media than the traditional Lame coefficients.

The diagonalized contrast source inversion approach for elastic wave inversion.

This study focuses on the inverse scattering of objects embedded in a homogeneous elastic background. The medium is probed by ultrasonic sources, and the scattered fields are observed along a receiver array. The goal is to retrieve the shape, location, and constitutive parameters of the objects through an inversion procedure. The problem is formulated using a vector integral equation. As is well-known, this inverse scattering problem is nonlinear and ill-posed. In a realistic configuration, this nonlinear inverse scattering problem involves a large number of unknowns, hence the application of full nonlinear inversion approaches such as Gauss-Newton or nonlinear gradient methods might not be feasible, even with present-day computer power. Hence, in this study we use the so-called diagonalized contrast source inversion (DCSI) method in which the nonlinear problem is approximately transformed into a number of linear problems. We will show that, by using a three-step procedure, the nonlinear inverse problem can be handled at the cost of solving three constrained linear inverse problems. The robustness and efficiency of this approach is illustrated using a number of synthetic examples.

Microwave tomography for functional imaging of extremity soft tissues: feasibility assessment.

It is important to assess the viability of extremity soft tissues, as this component is often the determinant of the final outcome of fracture treatment. Microwave tomography (MWT) and sensing might be able to provide a fast and mobile assessment of such properties. MWT imaging of extremities possesses a complicated, nonlinear, high dielectric contrast inverse problem of diffraction tomography. There is a high dielectric contrast between bone and soft tissue in the extremities. A contrast between soft tissue abnormalities is less pronounced when compared with the high bone-soft tissue contrast. The goal of this study was to assess the feasibility of MWT for functional imaging of extremity soft tissues, i.e. to detect a relatively small contrast within soft tissues in closer proximity to high contrast boney areas. Both experimental studies and computer simulation were performed. Experiments were conducted using live pigs with compromised blood flow and compartment syndrome within an extremity. A whole 2D tomographic imaging cycle at 1 GHz was computer simulated and images were reconstructed using the Newton, MR-CSI and modified Born methods. Results of experimental studies demonstrate that microwave technology is sensitive to changes in the soft tissue blood content and elevated compartment pressure. It was demonstrated that MWT is feasible for functional imaging of extremity soft tissues, circulatory-related changes, blood flow and elevated compartment pressure.

A multiplicative regularization approach for deblurring problems.

In this work, an iterative inversion algorithm for deblurring and deconvolution is considered. The algorithm is based on the conjugate gradient scheme and uses the so-called weighted L2-norm regularizer to obtain a reliable solution. The regularizer is included as a multiplicative constraint. In this way, the appropriate regularization parameter will be controlled by the optimization process itself. In fact, the misfit in the error in the space of the blurring operator is the regularization parameter. Then, no a priori knowledge on the blurred data or image is needed. If noise is present, the misfit in the error consisting of the blurring operator will remain at a large value during the optimization process; therefore, the weight of the regularization factor will be more significant. Hence, the noise will, at all times, be suppressed in the reconstruction process. Although one may argue that, by including the regularization factor as a multiplicative constraint, the linearity of the problem has been lost, careful analysis shows that, under certain restrictions, no new local minima are introduced. Numerical testing shows that the proposed algorithm works effectively and efficiently in various practical applications.

Contrast source inversion methods in elastodynamics.

In this paper a nonlinear inversion method is presented for determining the mass density of an elastic inclusion from the knowledge of how the inclusion scatters known incident elastic waves. The algorithm employed is an extension of the multiplicative regularized contrast source inversion method (MR-CSI) to elasticity. This method involves alternate determination of the mass density contrast and the contrast sources (the product of the contrast and the fields) in each iterative step. The simple updating schemes of the method allow the introduction of an extra regularization term to the cost functional as a multiplicative constraint. This so-called MR-CSI method (MR-CSI) has been proven to be very effective for the acoustic and electromagnetic inverse scattering problems. Numerical examples demonstrate that the MR-CSI method shows excellent edge preserving properties by robustly handling noisy data very well, even for more complicated elastodynamic problems.