Image Reconstruction for 3D Lung Imaging - Department of Systems ...

GCV
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
GCV(λ diag(H))
GCV(λHPF)
Local Minimums
10 −6 10 −4 10 −2 10 0 10 2
log10(λ)
Figure 4.8: GCV curves for different priors reconstructed on the same 576 element mesh
using the same tank data. Plot indicates shallowness of some GCV curves and consequent
potential difficulty of finding a clear minimum.
log(λ)
10 1
10 0
10 −1
λBestRes
λ NF=1/2 = 1.1721
λGCV
λNF=1 = 0.1350
10
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Noise (% of signal amplitude)
−2
Figure 4.9: λ versus noise for simulated data reconstructed on the 256 element mesh with
the Gaussian HPF prior. Simulated AWGN was added to the signal.
4.4.5 BestRes Results
As described in section 4.3.5, the BestRes method can use real or simulated data to calculate
the hyperparameter with similar results. Using real data has the potential to produce a
hyperparameter for the given configuration that is tailored to the equipment. In practice the
reconstructions obtained using this seemingly more accurate method are not qualitatively
improved over those that are generated using simulated data. For both tank and simulated
data using all 18 configurations the resolution curve exhibited a distinct minimum point at
which λBestRes could be calculated and subsequently used to obtain a “good” reconstruction.
It appears that resolution is a useful figure of merit for EIT reconstructions.
4.4.6 Fixed NF Results
With both the tank and simulated data λNF=1 was consistently located in the minimal
region of the resolution curve. Moreover λNF=1 always fell within the boundaries of the
hyperparameters selected by the experts (i.e. it was as consistent as the experts). Fixed NF
with NF = 1 always calculated a hyperparameter that resulted in a good reconstruction.
Our earlier experience using simulated, tank and clinical data has shown that noise figures
in the range 0.5 − 2 consistently lead to good reconstructions regardless of configuration
while the associated λ value can range over several orders of magnitude dependent on con-
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