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

Iteration 1
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Iteration 4
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Iteration 7
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Iteration 2
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Iteration 5
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Iteration 8
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TV
L2
phantom
Iteration 3
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Iteration 6
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Iteration 9
Figure 7.6: Profile plots of the originating contrast, TV, and ℓ 2 reconstructions. No Noise
added. Profiles are vertical slices through the middle of the reconstructed image.
7.4.5 Parameters
The PD-IPM method has two tuneable parameters β and λ. The value of β has a large
effect on convergence. Too large a value of β (greater than 10 −6 ) prevented convergence
to the desired “blocky” solution; the solution stabilized but showed smoothed features that
were not consistent with the edges obtained with smaller values of β. Ultimately it was
determined that the quickest convergence occurred when β was initialized to a small value
(we used 10 −12 ) and left unchanged. This was the method used in the results shown in this
paper.
With an iterative algorithm multiple values of the regularization hyperparameter, λ,
could be used for each iteration. In this work, for the TV algorithm, a different value was
used for λ0, in the initialization step (7.40) and for λi in the iterative steps (7.38). λ0
was selected using the BestRes method described in [52]. BestRes is an algorithm for objectively
calculating the hyperparameter for linearized one-step EIT image reconstruction
algorithms. This method suggests selecting a hyperparameter that results in a reconstruction
that has maximum resolution for an impulse contrast. Although TV is not intended
for use in imaging impulse type contrasts the first step of the algorithm requires solution
of the quadratic problem. In previous work the BestRes algorithm has provided λ values
based on an impulse contrast that has generalized well to non-impulse contrasts. See, for
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