Draft:ECTsim

ECTsim is an open-source software toolbox written in MATLAB designed primarily for measurement simulation and image reconstruction for electrical capacitance tomography (ECT), in industrial and biomedical aplications.

The name is an acronym for Electrical Capacitance Tomography Simulation. In the graphical logo, the letters E and s are replaced with the Greek letters ε (epsilon) and σ (sigma), which are symbols of permittivity and conductivity, two electrical properties of matter.

History
The project was launched in 2008 by prof. Waldemar T. Smolik in Data Acquisition and Processing Lab at Warsaw University of Technology. with a MATLAB code for numerical simulation and image reconstruction in 2D ECT. In 2013, the software was expanded to include a refined cartesian mesh with the finite element method for solving the forward problem. The first attempt to expand ECTsim to support three-dimensional simulations took place in 2017, using a hybrid method where some functions were written in C++ and called in MATLAB to achieve faster computations. However, the software was unintuitive to use and prone to errors. In 2020, a new version of ECTsim was developed, supporting both 2D and 3D problems. The new version uses an octree refined mesh and the finite volume method, and it is fully written in MATLAB. Since 2024, ECTsim has been publicly available on GitHub under the Apache 2.0 license

Numerical Modeling
ECTsim for numerical modeling provides a set of functions that, using geometric primitives and simple transformations, enable the creation of any 2D and 3D objects needed to model a measurement sensor for electrical tomography. These tools simplify the process of constructing complex models, making it easier for users to prepare detailed and accurate numerical simulations.

Forward Problem Solver
ECTsim utilizes the Finite Volume Method with quadtree and octree mesh refinement for 2D and 3D models, respectively. The software allows for the simulation of complex potential distributions, electric field distributions, and the preparation of sensitivity matrix. This capability enables the simulation of both conductance and capacitance measurements, providing comprehensive data for electrical capacitance tomography.

Image Reconstruction
The toolbox includes four fundamental image reconstruction algorithms: LBP, PINV, Landweber, and a semi-linear implementation of the Levenberg-Marquardt algorithm. These algorithms facilitate detailed image reconstruction, and the software can display mean square error norms obtained during the iterative algorithm, aiding in the assessment and improvement of reconstruction quality.

Advanced Visualization Methods
ECTsim is equipped with advanced methods for displaying both 2D and 3D images, including Multi-Planar Reconstruction (MPR), shaded surface, and slice visualization techniques. These methods support windowing, allowing users to customize the view and enhance the analysis of the reconstructed images, providing a robust tool for visual interpretation and analysis of tomography data.

Applications
ECTsim has found applications in both industrial and biomedical fields, including lung imaging, and investigation of brain stroke. In recent years, due to its very fast operation while maintaining high simulation accuracy, it has been used for preparing training datasets for machine learning. This is a valuable, particularly in scenarios where large and accurate datasets are crucial, like 3D image reconstruction.