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Electrical Impedance Tomography Using Evolutionary Computing: A Review
Published in D. P. Acharjya, V. Santhi, Bio-Inspired Computing for Image and Video Processing, 2018
Wellington Pinheiro dos Santos, Ricardo Emmanuel de Souza, Reiga Ramalho Ribeiro, Allan Rivalles Souza Feitosa, Valter Augusto de Freitas Barbosa, Victor Luiz Bezerra Arajo da Silva, David Edson Ribeiro, Rafaela Covello de Freitas
The experiments realized in this work were made using the tool EIDORS (Electrical Impedance Tomography and Diffuse Optical Tomography Reconstruction Software), a computational tool open sourced and used in EIT. It was developed starting in 1999 for MatLab (versions ≥ $ \ge $ 2008a) and Octave (versions ≥ $ \ge $ 3.6). EIDORS is characterized by providing several free, inverse problem resolution algorithms of EIT, for example: Gauss-Newton [2], GREIT [1], NOSER [15] non-trivial and Backprojection [45]. This tool can realize some, tasks of EIT such as the resolution of direct and inverse problems for any domain, or the graphical representation of a candidate vector to the solution in a mesh of triangular finite elements in order to visually evaluate the distribution of electrical conductivity.
Multiple inhomogeneity phantom imaging with a LabVIEW-based Electrical Impedance Tomography (LV-EIT) System
Published in Debatosh Guha, Badal Chakraborty, Himadri Sekhar Dutta, Computer, Communication and Electrical Technology, 2017
Tushar Kanti Bera, Sampa Bera, J. Nagaraju, Badal Chakraborty
Resistivity images are reconstructed from the boundary data using EIDORS using a symmetric FEM mesh discretizing the phantom domain (Fig. 4a). EIDORS, which is an open source software, aims to reconstruct the 2D-images from electrical or diffuse optical data. In the present study of the image reconstruction with EIDORS, the circular domains (diameter 228 mm) are discretized with a symmetric triangular element mesh containing 1968 elements and 1049 nodes (Fig. 4a–4b), is used in forward solution and inverse solution. The inverse problem is solved with applying the Levenberg-Marquardt Regularization (LMR) technique. The electrode positions are identified in FEM mesh in the algorithm and the boundary conditions are applied accordingly.
Diffuse Optical Imaging
Published in Helmut H. Telle, Ángel González Ureña, Laser Spectroscopy and Laser Imaging, 2018
Helmut H. Telle, Ángel González Ureña
Software. For the understanding and interpretation of DOI, there are two key ingredients: (1) the modeling of the photon transport in tissue and (2) the reconstruction of images from diffuse scattering measurements; these will be discussed in more detail in Section 20.3. The former is normally tackled via Monte Carlo methods or diffusion theory, based on the radiation transfer equation; for the latter, finite element methods (FEMs) are normally utilized. Over the past 20 years, many groups have developed sophisticated theoretical modeling approaches and written bespoke computer codes, many of them based on Matlab™ because of its wide use and its relative ease of graphical presentation of data. Certain ad hoc development and implementations of computer codes for DOI are still widespread. On the other hand, a few elegant open-source software packages are now available, which may ease the burden of having to rewrite vast segments of computer code, which in principle is common to many applications in DOI. Such complete packages are—without claiming completeness—EIDORS (Adler and Lionheart 2006), NIRFAST (Jermyn et al. 2013), and TOAST++ (Schweiger and Arridge 2014). EIDORS is based on Matlab™ code, and its goal was “to provide free software algorithms for forward and inverse modeling for… Diffusion-based Optical Tomography (DOT), in medical and industrial settings.” NIRFAST is also run within the Matlab™ environment. It is a FEM-based package for modeling NIR-light transport in tissue and includes (1) single wavelength absorption and scatter; (2) multiwavelength spectrally constrained models; and (3) fluorescence models. TOAST++ is written in C++ but also contains bindings for Matlab™ and Python™. It is a software suite for image reconstruction in DOT and contains a forward-solver module “using FEM for simulating the propagation of light in highly scattering, inhomogeneous biological tissues” and an inverse-solver module that “uses an iterative, model-based approach to reconstruct the unknown distributions of absorption and scattering coefficients in the volume of interest from boundary measurements of light transmission.” All three packages incorporate the capabilities to adapt the solvers to novel sample properties and geometries.
A polarization tensor approximation for the Hessian in iterative solvers for non-linear inverse problems
Published in Inverse Problems in Science and Engineering, 2021
F. M. Watson, M. G. Crabb, W. R. B. Lionheart
Our numerical experiments were implemented in Matlab using the developers version of the open-source EIT package EIDORS [45,46], which uses the complete electrode model outlined in Section 2.1. Polarization tensor Hessian reconstructions were benchmarked against a fairly standard non-linear Gauss–Newton method to solve the optimization problem in EIT as implemented by the EIDORS library function inv_solve_core. The functions and scripts used in this paper can also be obtained via the EIDORS developers SVN repository. This includes the polarization tensor Hessian approximation, the Neumann functions for a disc and free-space in 2D, as well as the inversion scheme. It also includes the calculation of the true Hessian via an adjoint method. Experiments were carried out on a 2D disc with radius with electrodes, of background conductivity . The meshes were created using the EIDORS function ng_mk_cyl_models, which calls routines from Netgen Mesher [47].
Non-convex ℓ p regularization for sparse reconstruction of electrical impedance tomography
Published in Inverse Problems in Science and Engineering, 2021
The forward model with CEM was based on the EIDORS toolkit for a linear finite element solver written in Matlab developed by Vauhkonen [36]. A 16 equally spaced electrode system is modelled surrounding two-dimensional circle meshes for simulations. We use constant injection current between adjacent electrodes and adjacent voltage measurement between all other electrodes. Two different finite elements meshes are used for the forward and inverse solvers to avoid inverse crimes. The forward solutions are generated with 1049 nodes and 1968 elements, and the inverse computations are implemented with coarse meshes of 279 nodes and 492 elements to reduce the computational burden. Since we do not perform experimentations, we should obtain the boundary voltage data relying on computer simulation. The noisy measurement data are generated in the form of where denotes the exact synthetic measurements, δ is a relative noise level, and n is the random variable following uniform distribution in [0,1].
An efficient one-step proximal method for EIT sparse reconstruction based on nonstationary iterated Tikhonov regularization
Published in Applied Mathematics in Science and Engineering, 2023
To do this, the details on the setting are required as follows: A 2D 16 equally-spaced electrodes system is modeled using the Matlab-based 2D EIDORS demo version developed by Vauhkonen [50], from which the boundary voltage data and sensitivity matrix can be calculated.Two sparse Phantom A and Phantom B shown in Figure 1, consisting of multiple various simple sharp inclusions at different locations and a homogeneous background with constant resistivity, are modelled for the simulation study. The higher (white inclusions) and lower (black inclusions) resistivity distribution values are set as 8.0 and 2.0 , respectively, and the background conductivity is 4 . Unless otherwise specified, all reconstruction images next will be displayed with the unified hotbars from 2 to 8.To avoid committing the ‘inverse crime’, the forward solutions are generated with 1049 nodes and 1968 elements, and the inverse computations are implemented with coarse meshes of 279 nodes and 492 elements.The noisy measurement data are generated in the form of where denotes the exact synthetic measurements, δ is a relative noise level, and n is the random variable following uniform distribution in [0,1]. Two noise levels, i.e. , are considered.NITR method with parameter sequence as in (19), with and q = 0.5. The iteration is terminated according to the discrepancy principal (22), with proper parameter estimate τ. The one-step proximal sparse evaluation is illustrated with .The relative error (RE) and the correlation coefficient (CC) are employed to evaluate the reconstruction performance quantitatively, given by where σ is the calculated conductivity distribution, is the real one, N is the total number of elements, and and are the mean values of σ and , respectively. It is noticed that a smaller value of RE and a larger value of CC reflect better reconstruction performance. The reconstruction image is closer to the real image when the value of CC is closer to 1.