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Error sensitivity
To test the error sensitivity of the inverse tomographic problem we
take the test model from section 3.1 and impose
errors in the projection/forward model/imaging process. Here the
sensitivity to two sources of errors will be discussed. The first
is in the sensitivity of the cameras and the second is in uncertainties
concerning the directions of the linesofsight. The
sensitivity errors are introduced by multiplying the modelled images
from the stations at 50 km north and 100 km south by 1.03 and the
model image from the station at 50 km south by 0.97, modelling an
uncertainty of 3 % in camera sensitivity. To test the
sensitivity to errors in orientation, the 1D images are randomly
shifted by one pixel for all stations simulating an angular uncertainty of
. The uncertainties are first applied separately and
finally together. The
imperfect 1D images are then used to make reconstructions with both
damped least square and the ART inversion. The result is that even for the perfect images the reconstructions are more coarse
than the auroral model, as can be seen in the upperleft panels of
Figure 3.8 and Figure 3.9. For the
nonperfect projections, the noise in the images makes the damped
least square reconstructions, in particular, more noisy but also the
ART reconstructions show artifacts manifested mainly as streaks in the
radial direction from the stations.
Figure 3.8:
Model test of the damped least square solution of the
tomographic problem using the model aurora shown in
Figure 3.3. Upperleft panel is a reconstruction
from perfect projections with a 1 % noise level. Upperright
panel is a reconstruction from projections with 3 % sensitivity
errors. Lowerleft panel is a reconstruction from projections
that have rotational errors. Lowerright panel is a
reconstruction from projections with errors in both sensitivity
and rotation.

Figure 3.9:
Model test of the algebraic reconstruction technique
(ART) solution of the tomographic problem with the model aurora
shown in Figure 3.3. Upperleft panel is a
reconstruction from perfect projections with a 1 % noise
level. Upperright panel is a reconstruction from projections
with 3 % sensitivity errors. Lowerleft panel is a
reconstruction from projections that have degrees rotational
errors. Lowerright panel is a reconstruction from projections
with errors in both sensitivity and rotation.

As can be seen, the errors in the reconstruction increase already at
these low levels of uncertainties in the forward model. Thus, in order
to obtain reconstructions of the aurora with sufficient quality for
making further analysis worthwhile, it is of vital importance to
achieve the necessary accuracy of the forward model.
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copyright Björn Gustavsson 20001024
