Image reconstruction for electromagnetic field visualization by an inverse problem solution

Abstract

The purpose of this article is to apply an inverse approach for image reconstruction during electromagnetic field visualization. The reconstruction of the images is formulated as an inverse problem. For the image color model, the Poisson equation with open boundary condition is imposed. The color source densities have been evaluated from the color distributions for electromagnetic field data set. The Generalized Vector Sampled Pattern Matching method is applied to solve an ill posed linear system of equations for the corresponding inverse problem. The new color distributions are generated and visualized using the obtained color source densities. With the proposed inverse approach the dark parts of the images can be reduced or completely removed. This article collects several examples for electromagnetic field visualization of the most commonly used sensor coil. Visualization techniques facilitate the examination of unknown data sets and play an integral role in modeling and investigation of electromagnetic devices. The field distribution is of main importance considering many identification, NDT or EMC problems (1). The Finite Element Method (FEM) or Boundary Element Method (BEM) are usually used for investigation of varies electromechanical devices. The results obtained are visualized using different visualization techniques. Sometimes the images are with not good quality or the data obtained do not correspond to the area of interest. To obtain new results, new FEM or BEM calculations are required which are accompanied by a lot of efforts and computational time. This is one of the main difficulties building interactive simulation and visualization systems. Many problems in medical diagnosis, as well as in industry quality control, require reducing the dark spots of the images. In order to reconstruct the images we propose an approach using formulation and solution of the inverse problem over the image. The image quality depends on the image resolution and color distribution. The image is considered as a 2D-distribution of color components - Red, Green, and Blue (RGB). The 2D-Poisson equation in Cartesian coordinate system is imposed to be satisfied by each of RGB color components with homogeneous open boundary conditions. In order to determine the color component distribution in the image part of interest we calculate the distribution of color component source densities utilizing Green functions. The inverse problem for color source densities