Visualizing and analyzing dynamic processes in 3 dimensions is an increasingly important topic, e.g. in geo-
sciences , . High-resolution CT-scanning is a suitable technique for this, as it is non-destructive and
therefore does not hinder the dynamic process while it is ongoing.
In order to reconstruct a 4D-CT scan, i.e. create a 4D volume from the projection images of the CT scan,
the set of projection images is divided into smaller subsets, each representing a small time frame. Each subset
is reconstructed separately with a traditional CT reconstruction technique, which yields a 3D volume. The
combination of all these 3D reconstructions is the resulting 4D volume.
However, these reconstruction techniques assume a static sample. Motion artefacts are introduced when this
assumption is invalid, which is the case for the small time frames over which each 3D volume is reconstructed.
To minimize the motion artefacts, the scan is performed at high speed and therefore suers from lower statistics
hence higher noise. The resulting reconstruction quality for the 4D volume is insucient for fast processes.
One method to improve reconstruction quality is using a priori knowledge. Of the two most used reconstruc-
tion algorithms, the iterative reconstruction scheme is best suited for this. In this research, the simultaneous
algebraic reconstruction technique or SART  is used and adapted to take prior knowledge into account.
The most well-known way to incorporate prior knowledge into an iterative reconstruction algorithm is an initial
volume. The iterative reconstruction will not start from an empty volume, but from an already known volume
resembling the sample. This can be a high quality CT scan from before the dynamic process was initiated or
a model for for example a 3D printed sample. Using an initial volume instead of an empty volume already
presents a great improvement .
Other forms of a priori knowledge, such as the continuity of changes  or the incompressibility of a uid
combined with static regions in the sample , can also be included. In this work, we supplement the initial
volume with the prior knowledge of the locations in the sample where the dynamic process is most likely to
occur, while also leaving some room for error in this prior knowledge.
2. EXPERIMENTAL METHOD
In order to include the locations of change in the reconstruction, we use a weight volume. This is a 3D volume
of the same size as the reconstruction volume. Each voxel has a weight, a number that indicates how likely this
voxel is present in a dynamic region. This weight determines what fraction of the backprojection of an X-ray
is assigned to this voxel as compared to the other voxels on the path of that X-ray. A higher weight means the
voxel receives more of this backprojection and therefore this voxel will change more from its value in the initial
We demonstrate weighted backprojection on a 4D-CT dataset from geological research.
This dataset considered uid ow through a Bentheimer sandstone. This experiment was performed to inves-
tigate the intrusion of oil into a water-lled porous rock, with relevance to the study of groundwater pollution
and petroleum reservoirs [1, 8]. The sandstone was shaped roughly cylindrical, with a height of about 10 mm
and a diameter of about 6 mm.
The experimental data from this sandstone were acquired using the EMCT micro-CT scanner . One initial
high quality scan of the porous rock was used as a basis for the weight volume, since the dynamic process occurs
inside the pores.
In gure 1 a weighted backprojection reconstruction is compared to a normal reconstruction and one from an
initial volume. It is clearly visible that the weighted backprojection already shows lled pores (black), while
both other reconstructions need more data. Therefore, the weighted backprojection converges much faster and
can handle having less projections available.