Sushko I. Visualization of surface conductivity distribution of tomographic sections by conductivity zones method

The development of inverse problem solving methods and algorithms (visualization of inhomogeneity distribution inside phantom by measured voltages on contour outline) using proposed by author conductivity zones method is held. It allows significantly to reduce the order of derivative matrices from transfer resistances (nodal voltages) on surface zones conductivities. It allows to simplify the inhomogeneity visualization by reducing the number of arithmetic operations in iterative process. Solving systems of equations by ill-conditioned derivatives matrices is realized using regularization method by A.M. Tykhonov. Methods for iterative regularization process replacing by process with logarithmic step or compact method with inversion of the corresponding matrix. The algorithm of modification method for Electrical Impedance Tomography forward problem solution considering the phantom partition on zones is adapted on the basis of the finite element method. It allows to calculate the inverse matrix coefficients of the system of phantom equilibrium equations directly growing relations between finite elements. It provides high accuracy and performance of analysis for phantoms with hundreds . thousands of finite elements. Square and cubic updated models of finite elements are proposed. The analysis software allows to assess the sensitivity of voltages on contour outline from sizes, localization and normalized relative to the background inhomogeneity conductivities. Proposed conductivity zones method is the complex finite element creation. Synthesis (visualization) problem with certain connection of independent current source for 6-30 orders of derivative matrices is solved. The conductivities obtained for each from 8-32 source positions (using 8-32 measured electrodes) are summarized with partial solutions superposition. The inverse problem solution is reduced to 8-32 problems with 6-30 orders instead of the problem with 1000 order. Iteration regularization method to inverse the derivative matrices from transfer resistances (nodal voltages) on surface zones conductivities is used. The logarithmic step or compact method algorithms are developed in this work to replace 1000 and more iterations in regularization method by nearly 10- 20 steps using logarithmic step regularization algorithm or one inversion of matrix with 6 -30 order. The estimation of reconstruction by conductivity zones method using measured data on the Electrical Impedance Tomography layout is conducted. The assessment of ability to obtain the reliable results (depending on inhomogeneity localization in phantom, itЃfs sizes and surface conductivity) by constructing and training normal orthogonal classifier is shown. The developed methods provide the inhomogeneity identification (contrast with the background >2) with area > 5% from total phantom area (the worst sensitivity) in the center of phantom and with area > 1 - 2 % (the best sensitivity) near the edge of phantom.