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Register a new userIncorporating a Spatial Prior into Nonlinear D-Bar EIT imaging for Complex Admittivities
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Electrical Impedance Tomography (EIT) aims to recover the internal conductivity and permittivity distributions of a body from electrical measurements taken on electrodes on the surface of the body. The reconstruction task is a severely ill-posed nonlinear inverse problem that is highly sensitive to measurement noise and modeling errors. Regularized D-bar methods have shown great promise in producing noise-robust algorithms by employing a low-pass filtering of nonlinear (nonphysical) Fourier transform data specific to the EIT problem. Including prior data with the approximate locations of major organ boundaries in the scattering transform provides a means of extending the radius of the low-pass filter to include higher frequency components in the reconstruction, in particular, features that are known with high confidence. This information is additionally included in the system of D-bar equations with an independent regularization parameter from that of the extended scattering transform. In this paper, this approach is used in the 2-D D-bar method for admittivity (conductivity as well as permittivity) EIT imaging. Noise-robust reconstructions are presented for simulated EIT data on chest-shaped phantoms with a simulated pneumothorax and pleural effusion. No assumption of the pathology is used in the construction of the prior, yet the method still produces significant enhancements of the underlying pathology (pneumothorax or pleural effusion) even in the presence of strong noise.
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Objective: To develop, and demonstrate the feasibility of, a novel image reconstruction method for absolute Electrical Impedance Tomography (a-EIT) that pairs deep learning techniques with real-time robust D-bar methods. Approach: A D-bar method is paired with a trained Convolutional Neural Network (CNN) as a post-processing step. Training data is simulated for the network using no knowledge of the boundary shape by using an associated nonphysical Beltrami equation rather than simulating the traditional current and voltage data specific to a given domain. This allows the training data to be boundary shape independent. The method is tested on experimental data from two EIT systems (ACT4 and KIT4). Main Results: Post processing the D-bar images with a CNN produces significant improvements in image quality measured by Structural SIMilarity indices (SSIMs) as well as relative $ell_2$ and $ell_1$ image errors. Significance: This work demonstrates that more general networks can be trained without being specific about boundary shape, a key challenge in EIT image reconstruction. The work is promising for future studies involving databases of anatomical atlases.
The first numerical implementation of a D-bar method in 3D using electrode data is presented. Results are compared to Calderons method as well as more common TV and smoothness regularization-based methods. D-bar methods are based on tailor-made non-linear Fourier transforms involving the measured current and voltage data. Low-pass filtering in the non-linear Fourier domain is used to stabilize the reconstruction process. D-bar methods have shown great promise in 2D for providing robust real-time absolute and time-difference conductivity reconstructions but have yet to be used on practical electrode data in 3D, until now. Results are presented for simulated data for conductivity and permittivity with disjoint non-radially symmetric targets on spherical domains and noisy voltage data. The 3D D-bar and Calderon methods are demonstrated to provide comparable quality to their 2D CGO counterparts, and hold promise for real-time reconstructions.
We propose the variable selection procedure incorporating prior constraint information into lasso. The proposed procedure combines the sample and prior information, and selects significant variables for responses in a narrower region where the true parameters lie. It increases the efficiency to choose the true model correctly. The proposed procedure can be executed by many constrained quadratic programming methods and the initial estimator can be found by least square or Monte Carlo method. The proposed procedure also enjoys good theoretical properties. Moreover, the proposed procedure is not only used for linear models but also can be used for generalized linear models({sl GLM}), Cox models, quantile regression models and many others with the help of Wang and Leng (2007)s LSA, which changes these models as the approximation of linear models. The idea of combining sample and prior constraint information can be also used for other modified lasso procedures. Some examples are used for illustration of the idea of incorporating prior constraint information in variable selection procedures.
Objective: Absolute images have important applications in medical Electrical Impedance Tomography (EIT) imaging, but the traditional minimization and statistical based computations are very sensitive to modeling errors and noise. In this paper, it is demonstrated that D-bar reconstruction methods for absolute EIT are robust to such errors. Approach: The effects of errors in domain shape and electrode placement on absolute images computed with 2D D-bar reconstruction algorithms are studied on experimental data. Main Results: It is demonstrated with tank data from several EIT systems that these methods are quite robust to such modeling errors, and furthermore the artefacts arising from such modeling errors are similar to those occurring in classic time-difference EIT imaging. Significance: This study is promising for clinical applications where absolute EIT images are desirable, but previously thought impossible.
The mathematical problem for Electrical Impedance Tomography (EIT) is a highly nonlinear ill-posed inverse problem requiring carefully designed reconstruction procedures to ensure reliable image generation. D-bar methods are based on a rigorous mathematical analysis and provide robust direct reconstructions by using a low-pass filtering of the associated nonlinear Fourier data. Similarly to low-pass filtering of linear Fourier data, only using low frequencies in the image recovery process results in blurred images lacking sharp features such as clear organ boundaries. Convolutional Neural Networks provide a powerful framework for post-processing such convolved direct reconstructions. In this study, we demonstrate that these CNN techniques lead to sharp and reliable reconstructions even for the highly nonlinear inverse problem of EIT. The network is trained on data sets of simulated examples and then applied to experimental data without the need to perform an additional transfer training. Results for absolute EIT images are presented using experimental EIT data from the ACT4 and KIT4 EIT systems.
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