In Electrical Impedance Tomography (EIT) the distribution of conductivity
inside a container is sought by applying specified currents (or voltages) at
some parts of the container surface, and performing measurements of the voltage
(or current) at some other parts. The equations for the electric field then
provide relationships between the conductivity distribution inside the domain
and the measured voltages and currents. Different types of materials have
different conductivity, and the availability of a conductivity map provides an
image of the material distribution in the container.
2DynaEIT is a suite of efficient and accurate algorithms for solution of the
inverse and forward EIT problems. These were developed under Phase I and Phase
II SBIR contracts with the National Science Foundation. The inverse problem is
the problem of image reconstruction using the measured voltages and/or currents,
while the forward problem is the problem of determination of voltage and current
distribution for known conductivity distribution in the imaged domain.
We have developed CPU-efficient methods, such as the Dipole Approximation
(DA), and the Singular Boundary Element Method (Singular BEM). These allow
one to solve rapidly the forward EIT problem in 2 and 3 dimensions. This enables
application of multi-dimensional minimization procedures, such as Powell's
Direction Set Method, Downhill Simplex Method, Conjugate Gradient Method, and
Genetic Algorithms, for solution of the inverse problem, which requires
thousands of calls of the forward problem solver. We also applied multi-objective
minimization based on Pareto sets.
The two and three-dimensional EIT algorithms that we have developed can be
applied for medical imaging, multiphase flows imaging encountered in chemical,
oil and gas, energy, and aerospace industries, non-destructive evaluation of
structures and materials, imaging of underground water paths and container
leakage, archaeology, detection of buried objects, chemical reactive flows, and
Application areas of EIT software are not limited by imaging based on
electrical properties. Since our methods of solution are based on the solution
of the classical Laplace, Poisson, and Helmholtz equations which describe a wide
variety of physical phenomena, including filtration, acoustical, optical,
thermal, and other processes, the developed software can be adjusted for such
problems as evaluation of oil and gas deposits, based on log data, seismic
imaging, and imaging of temperature and pressure fields in various industries.
We also can work on solution of similar user defined forward and inverse
problems of multidimensional imaging.