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  • EIT with the D-bar method: smooth and radial case

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Now we are ready to reconstruct the conductivity. Download the routines tBIErecon_comp.m and DB_oper.m,
and run tBIErecon_comp.m.

You can look at the reconstruction using the routine recon_plot.m. You should see something like this:

Image Added

Here we used R=4, so the reconstruction is not very close to the original. Try setting M=8 and R=7 in 
tBIErecon_comp.m and see what recon_plot.m produces then.

Note carefully that although we used the rotational symmetry of the conductivity to speed up some of the above 
computations, the solution of the D-bar equation is a two-dimensional process, not one-dimensional. 
We did choose the reconstruction points along the positive x1-axis for convenience, but any planar point x 
could be chosen. Also, note that the reconstruction at one x point is completely independent from the reconstruction 
at another point, so the D-bar method allows region-of-interest imaging and trivial parallellization.

You can experiment with the truncation radius R. When you use tBIE computed using the boundary integral equation, 
you can take R up to 7 with no problems. However, when R is so large that the bad-quality parts of the above magenta 
plot are being used, the reconstruction will be bad.

You can take the experiment further by using tLS instead of tBIE; then you can push the reconstruction to higher 
values of R. Also, you can replace the low-quality tLS values near k=0 with the higher-quality tBIE.