LIMITACIONES

In this thesis, two reconstruction algorithms were evaluated. There are many more reconstruction algorithms with various regularization, including statistical in- version. The statistical inversion method will be used to reconstruct the experimental data used in this thesis, and the results will be compared.

The data used in this thesis was from cementitious materials of the civil engi- neering field. EIT has many other applications, the most prominent being the medical field. Thus evaluation of these algorithms with medical data is important.

As discussed before, selection of the best hyperparameter is a crucial element of reconstruction of EIT data, and there is no single method to guarantee optimal, or consistent hyperparameter selection. Future work is needed to develope better, if not optimal hyperparameter selection methods.

Appendix A

A Starting Guide to EIDORS

EIDORS runs in Matlab and uses NETGEN meshing software to create the finite element mesh. Windows and linux are preferred operating systems for EIDORS. EIDORS can also run in Octave, but it is much more difficult to arrange directories correctly.

To use EIDORS for an EIT problem, the first step is to create the geometry of the object. For simple geometries, there are built-in functions such as

”ng mk cyl models.” For more complex geometries, you must call Netgen directly. Netgen objects are created by unions and intersections of basic shapes (spheres, rect- angles, cylinders). The ”-maxh” command allows for different mesh sizes for different parts of the object.

Next, define the electrode positions and shapes. These can be defined individ- ually, but for most EIT problems, electrodes are equally spaced and of the same size, so you can use the function ”ng mk cyl models(cyl shape, elec pos, elec shape).” ”cyl shape” has inputs {height, radius}. If height=0, then a 2D object is created. ”elec pos” has inputs {n electrodes per plane, m number of planes}, which will cre- ate m rings of n equally spaced electrodes (for 2D, m=1). ”elec shape has inputs

{width,height} where height=0 produces circular electrodes. Both width=0 and

height=0 produce point electrodes. If point electrodes are used, the complete elec- trode model is not used, as contact impedance would not exist.

Next, define the injection and measurement patterns with the function ”mk stim patterns.” this function has inputs {number of electrodes, number of rings, injection, measurement, options, amplitude}. Injection has many options, including adjacent, opposite, and trigonometric patterns. Measurement has the same options as injection, with multiple measurements being made for each injection pattern. The

”Options” field is used to tell EIDORS not to measure on the current carrying elec- trodes with the string 0no meas current0. ”Amplitude” is the applied current in Amps.

Lastly, set the conductivity of the geometry. First, set the background conduc- tivity using ”mk image”, which has inputs {fwdmodel, conductivity}. For nonhomo- geneous regions, use ”elem select” to define different regions, and call ”elem data” to change the conductivity of that region.

Now, all of the aspects of the forward problem are set, so use ”f wd solve” to solve for the voltages on the electrodes, which is the simulated data.

For the inverse model, set the geometry, injection and measurement patterns, solver, hyperparameter value, and background conductivity (prior). Set

”imdl.f wd model = f mdl” to use the same geometry and patterns as was used in the forward model. The function ”inv solve” solves the inverse problem, with inputs invmodel, voltage vector. The output is the reconstructed image, and a vector of conductivity values. The accuracy of the reconstruction can be obtained by comparing the reconstructed image with the true conductivity distribution.

If you run into problems using EIDORS, the first step is to check both the EIDORS and NETGEN documentation for troubleshooting, [1] [13]. If problems persist, search the EIDORS mailing list by keyword. If more help is needed, you can send an email to the developers’ mailing list; they usually are prompt in responding.

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