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@phdthesis{faucris.296586737,
abstract = {The mathematical model of computed tomography data acquisition shows that
every such measurement contains a degree of redundancy. This redundancy can
be used to formulate data consistency conditions which enable quantifying how
accurately a measurement fulfills the mathematical model. This enables compensating
for inaccuracies in the measurement process by formulating artifact compensation
as optimization problems of an objective function based on such data consistency
conditions.
In the course of this thesis, various methods to deal with different types of
such inaccuracies in the measurement have been proposed. One type of inaccuracy
arises due to the simplified physical model of computed tomography reconstruction
which assumes a mono-chromatic X-ray source. This leads to an effect commonly
named beam hardening. To compensate artifacts from this beam hardening effect
a projection-based algorithm named the Empirical Cupping Correction using the
Epipolar Consistency Condition (ECC 2 ) algorithm is introduced. It uses a recently
proposed data consistency condition called the Grangeat data consistency condition to
formulate an efficient procedure to estimate parameters of an appropriate compensation
model. This compensation model is derived to be physically plausible by mathematical
analysis of the beam hardening effect.
This method is extended in a second algorithm named the Multi-material ECC 2
(MECC 2 ) algorithm to incorporate the possibility to compensate artifacts caused
by the different energy dependencies of the linear attenuation coefficient of different
materials. Efficient parameter estimation techniques and methods for physically
plausible constraints on the compensation function are also presented.
Another category of inaccuracies in the measurement are caused by inaccurate
knowledge of the acquisition geometry or rigid movement of the imaged object. A
general strategy to solve both problems is to estimate the geometry of the acquisition
projection-based. However, this is difficult for X-ray imaging modalities because
standard techniques from computer vision can not be translated straightforward
to this setting. This is caused by the fact, that computer vision algorithms rely
on identifying corresponding points in multiple pictures of the same scene as a
fundamental step. This is very hard in X-ray imaging due to the different image
formation model. To solve this issue a method to estimate the relative geometry of
two views is introduced and methods to estimate a projective reconstruction based on
multiple pairwise geometry estimates.