scholarly journals Shape optimizationviaa levelset and a Gauss-Newton method

2019 ◽  
Vol 25 ◽  
pp. 3
Author(s):  
Jérôme Fehrenbach ◽  
Frédéric de Gournay
Keyword(s):  
Newton Method ◽  
General Framework ◽  
Electrical Impedance ◽  
Level Set Methods ◽  
Natural Extension ◽  
Least Square ◽  
Shape Derivative ◽  
Impedance Tomography ◽  
Quadratic Functionals ◽  
Compliance Problem

In the context of shape optimization via level-set methods, we propose a general framework for a Gauss-Newton method to optimize quadratic functionals. Our approach provides a natural extension of the shape derivative as a vector field defined in the whole working domain. We implement and discuss this method in two cases: first a least-square error minimization reminiscent of the Electrical Impedance Tomography problem, and second the compliance problem with volume constraints.

scholarly journals Comparison of Selected Machine Learning Algorithms for Industrial Electrical Tomography

Sensors ◽  
2019 ◽  
Vol 19 (7) ◽  
pp. 1521 ◽  
Author(s):  
Tomasz Rymarczyk ◽  
Grzegorz Kłosowski ◽  
Edward Kozłowski ◽  
Paweł Tchórzewski
Keyword(s):  
Machine Learning ◽  
Electrical Impedance Tomography ◽  
Newton Method ◽  
Electrical Impedance ◽  
Learning Algorithms ◽  
Machine Learning Algorithms ◽  
Electrical Tomography ◽  
Learning Methods ◽  
Impedance Tomography ◽  
Machine Learning Methods

The main goal of this work was to compare the selected machine learning methods with the classic deterministic method in the industrial field of electrical impedance tomography. The research focused on the development and comparison of algorithms and models for the analysis and reconstruction of data using electrical tomography. The novelty was the use of original machine learning algorithms. Their characteristic feature is the use of many separately trained subsystems, each of which generates a single pixel of the output image. Artificial Neural Network (ANN), LARS and Elastic net methods were used to solve the inverse problem. These algorithms have been modified by a corresponding increase in equations (multiply) for electrical impedance tomography using the finite element method grid. The Gauss-Newton method was used as a reference to machine learning methods. The algorithms were trained using learning data obtained through computer simulation based on real models. The results of the experiments showed that in the considered cases the best quality of reconstructions was achieved by ANN. At the same time, ANN was the slowest in terms of both the training process and the speed of image generation. Other machine learning methods were comparable with the deterministic Gauss-Newton method and with each other.

A Fast Image Reconstruction Algorithm for EIT Based on Wavelet Analysis and LSQR

2014 ◽  
Vol 654 ◽  
pp. 341-345
Author(s):  
Ying Zhi Sun ◽  
Jian Ming Wang ◽  
Qi Wang
Keyword(s):  
Image Reconstruction ◽  
Electrical Impedance ◽  
Reconstruction Algorithm ◽  
Scale Space ◽  
Least Square ◽  
Qr Factorization ◽  
Impedance Tomography ◽  
Image Reconstruction Algorithm ◽  
Low Dimension ◽  
2D And 3D

The LSQR algorithm is always used to solve the inverse problem of electrical impedance tomography (EIT). However, it always has relatively low reconstruction speed. In this paper, WALSQR (wavelet multi-resolution based Least Square QR-factorization) algorithm is proposed for EIT imaging. With the aid of wavelet transformation, the LSQR solution is obtained in the low-dimension scale space, where important information on the reconstructed image is contained. Hence the computational complexity of reconstruction is reduced without affecting the image quality. In order to verify the effectiveness of the new method, experiments of 2D and 3D EIT imaging are conducted. It lays the foundation for the study of 3D dynamic EIT image reconstruction algorithm.

scholarly journals TOPOLOGICAL ALGORITHMS TO SOLVE INVERSE PROBLEM IN ELECTRICAL TOMOGRAPHY

2017 ◽  
Vol 7 (1) ◽  
pp. 55-58
Author(s):  
Tomasz Rymarczyk
Keyword(s):  
Inverse Problem ◽  
Level Set ◽  
Optimization Problems ◽  
Level Set Methods ◽  
Topological Derivative ◽  
Optimization Approach ◽  
Shape Derivative ◽  
Electrical Tomography ◽  
Impedance Tomography ◽  
Material Derivative

In this paper, there were investigated topological algorithms to solve the inverse problem in electrical tomography. The level set method, material derivative, shape derivative and topological derivative are based on shape and topology optimization approach to electrical impedance tomography problems with piecewise constant conductivities. The cost of the numerical algorithm is enough good, because the shape is captured on a fixed grid. The proposed solution is initialized by using topological sensitivity analysis. Shape derivative and material derivative (or topological derivative) have been incorporated with level set methods to investigate shape optimization problems.

Image Theory for Electrical Impedance Tomography

2011 ◽  
pp. 117-144
Author(s):  
P. D. Einziger ◽  
M. Dolgin
Keyword(s):  
Inverse Problem ◽  
Electrical Impedance Tomography ◽  
Electrical Impedance ◽  
Physical Phenomenon ◽  
Stable Solution ◽  
Least Square ◽  
Image Theory ◽  
Reconstruction Procedure ◽  
Impedance Tomography ◽  
Piecewise Constant Conductivity

Image reconstruction by electrical impedance tomography is, generally, an ill-posed nonlinear inverse problem. Regularization methods are widely used to ensure a stable solution. Herein, we present a novel electrical impedance tomography algorithm for reconstruction of layered biological tissues with piecewise continuous plane-stratified profiles. The algorithm is based on the reconstruction scheme for piecewise constant conductivity profiles, which utilizes Legendre expansion in conjunction with improved Prony method. This reconstruction procedure, which calculates both the locations and the conductivities, repetitively provides inhomogeneous depth discretization, (i.e., the depths grid is not equispaced). Incorporation of this specific inhomogeneous grid in the widely used mean least square reconstruction procedure results in a stable and accurate reconstruction, whereas, the commonly selected equispaced depth grid leads to unstable reconstruction. This observation establishes the main result of our investigation, highlighting the impact of physical phenomenon (image theory) on electrical impedance tomography, leading to a physically motivated stabilization of the inverse problem, (i.e., an inhomogeneous depth discretization renders an inherent regularization of the mean least square algorithm).

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