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

to noise however both algorithms produce useful 2D reconstructions at realistic noise
levels.
The ability of PD-IPM algorithm to reconstruct edges in 3D models was not satisfactorily
determined. The PD-IPM algorithm reconstructs the conductivity in the
elemental basis. The complexity of the elemental solution limits the resolution of
the finite element model. Thus the capability of determining 3D TV performance is
limited to relatively coarse FEMs that may limit the performance of the algorithm.
Further work is required to enable the solution of higher resolution 3D models in order
to evaluate the performance of PD-IPM for 3D lung imaging.
In summary, TV regularised reconstructions are considerably more expensive to calculate
than quadratic reconstructions, however the TV PD-IMP algorithm is able to
compute 2D non-smooth reconstructions in the presence of moderate noise, and is
therefore of practical use in certain applications. It is not currently recommended for
use with 3D lung imaging.
The main contribution of this objective was the improvement in convergence of the
PD-IPM algorithm and the evaluation of the algorithm’s performance in 2D and 3D
applications.
This work is described in the article “Total Variation Regularization for EIT,” by
Borsic, Graham, Lionheart, and Adler. Chapter 7 is a copy of the a manuscript
in preparation for submission to IEEE Transactions on Medical Imaging. This is a
collaborative work. The development of the PD-IPM algorithm, it’s explanation and
implementation are the original work of Andrea Borsic and can be found in [23]. The
analysis of the algorithm’s performance, including the improvement in convergence,
the simplification of the β decay schedule as well as the design and execution of
the algorithm’s performance evaluation and subsequent conclusions are the original
contribution of this thesis. Dr Adler and Dr Lionheart are the PhD supervisors of
Graham and Borsic respectively.
1.4.2 Miscellaneous Contributions
The background research for this thesis is contained in chapters 2 and 3. These chapters
include, in one place, the complete development of the finite element solution of the forward
problem from Laplace’s equation through to the finite element solution. We are unaware of
the existence of a similar end-to-end derivation elsewhere in the EIT literature.
Numerical simulation of conductivity data permits the rapid development of imaging
algorithms than would not be possible if researchers were restricted to only using lab data.
However, many EIT papers rely strictly on simulated data to make conclusions. Scientific
and engineering results based on simulations are valuable but must be verified with empirical
(lab) data. Therefore a collateral objective of this thesis is to verify simulated results with
empirical data collected in our lab. Thus, where possible, the conclusions presented in this
thesis are verified using the Goe-MF II adjacent stimulation tomography system (Viasys
Healthcare, Höchberg, Germany).
The impulse function and point spread function are basic tools of signal processing for
linear systems. Neither the impulse function nor point spread function are mentioned in the
EIT literature perhaps because EIT is a non-linear modality. In this thesis pseudo-impulse
phantoms are introduced and used with EIT. In section 4.3.5 we first introduce the Blur
Radius measure which is an analog of the point spread function adapted for EIT using
finite element meshes. The argument for the use of pseudo-impulse functions in algorithm
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