The objective of the Electrical Impedance and Diffuse Optical Reconstruction Software project is to develop freely available software that can be used to reconstruct electrical or optical material properties from boundary measurements. Nonlinear and ill posed problems such as electrical impedance and optical tomography are typically approached using a finite element model for the forward calculations and a regularized nonlinear solver for obtaining a unique and stable inverse solution. Most of the commercially available finite element programs are unsuitable for solving these problems because of their conventional inefficient way of calculating the Jacobian, and their lack of accurate electrode modelling. A complete package for the two-dimensional EIT problem was officially released by Va uhkonen et al at the second half of 2000. However most industrial and medical electrical imaging problems are fundamentally three-dimensional. To assist the development we have developed and released a free toolkit of Matlab routines which can be employed to solve the forward and inverse EIT problems in three dimensions based on the complete electrode model along with some basic visualization utilities, in the hope that it will stimulate further development. We also includ ead erivation of theformula for the Jacobian (or sensitivity) matrix based on the complete electrode model.

This study addresses the issue of structural damage identification and location in carbon fiber reinforced polymer plates using electrical measurements. Electrical resistance tomography is presented as a method for structural damage localization in composite parts. A set of electrodes is fixed on the edges of the part and combinations of DC current injections and voltage measurements are applied to the system. The change of voltage between different times in the part’s service life (e.g. start and degraded) are monitored. These sets of measurements are used as input to inversely calculate conductivity maps for the complete composite part and thus indirectly assess its structural health. Such processes are inherently ill-posed. Data post-processing approaches are proposed here to diminish this uncertainty and to conclude to an optimally converge solution of the inverse problem. To assist the process, a material-originating mathematical constraint is introduced. The method is applied on carbon fiber reinforced polymer plates for different damage modes. Experimental recordings show that the analysis of electrical fields allows detecting the presence of damage. Discontinuities as small as 0.1% of the inspected area can be sensed. The proposed data post-processing techniques were applied and conductivity maps were calculated. The results show that using these techniques locating damage is possible with less than 10% error. Material-based constraints greatly enhance the prediction of the data post-processing techniques. It is believed that by overcoming certain implementation issues, electrical resistance tomography could evolve in the direction of a non-destructive evaluation or a structural health monitoring technique for composite structures.

Image reconstruction in electrical impedance tomography is an ill-posed nonlinear inverse problem. Linearization techniques are widely used and require the repeated solution of a linear forward problem. To account correctly for the presence of electrodes and contact impedances, the so-called complete electrode model is applied. Implementing a standard finite element method for this particular forward problem yields a linear system that is symmetric and positive definite and solvable via the conjugate gradient method. However, preconditioners are essential for efficient convergence. Preconditioners based on incomplete factorization methods are commonly used but their performance depends on user-tuned parameters. To avoid this deficiency, we apply black-box algebraic multigrid, using standard commercial and freely available software. The suggested solution scheme dramatically reduces the time cost of solving the forward problem. Numerical results are presented using an anatomically detailed model of the human head.

Acoustic tomography can be used to measure the temperature field from the time-of-flight (TOF). In order to capture real-time temperature field changes and accurately yield quantitative temperature images, two improvements to the conventional acoustic tomography system are studied: simultaneous acoustic transmission and TOF collection along multiple ray paths, and an offline iteration reconstruction algorithm. During system operation, all the acoustic transceivers send modulated and filtered wideband Kasami sequences simultaneously to facilitate fast and accurate TOF measurements using cross-correlation detection. For image reconstruction, the iteration process is separated and executed offline beforehand to shorten computation time for online temperature field reconstruction. The feasibility and effectiveness of the developed methods are validated in the simulation study. The simulation results demonstrate that the proposed method can reduce the processing time per frame from 160 ms to 20 ms, while the reconstruction error remains less than 5%. Hence, the proposed method has great potential in the measurement of rapid temperature change with good temporal and spatial resolution.

This study addresses the numerical treatment applied to the singular values of the sensitivity matrix in the presence of noisy measurements, subsequently suggesting electrode configurations that provide sensitivities with improved characteristics. We begin by examining the impact of the individual singular values on the spatial resolution of the image and then proceed to express the generalized Tikhonov regularization in terms of the generalized singular value decomposition in order to demonstrate how the reconstructed image is synthesized from the individual energy components. The electrode segmentation scheme is then introduced as af easible configuration offering efficient and improved resolution impedance imaging. Finally, the regularized total least squares algorithm is implemented to provide the linear step solution within Newton's iterative scheme. Images of several reconstructed inhomogeneities are presented, using simulated measurements obtained from the segmented electrodes system.