Improving the reconstruction of dynamic processes by including prior knowledge

Visualizing and analyzing dynamic processes in 3 dimensions is an increasingly important topic. 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 advancing. However, CT reconstruction algorithms, which reconstruct a 3D volume from a series of projection images, assume a static sample. Motion artefacts are introduced when this assumption is invalid. This is usually solved by dividing the set of projection images in smaller subsets, each representing a time frame in which the change to the sample is assumed to be sufficiently small. Each subset can be reconstructed separately. However, due to the small size of the subsets and/or the high speed (and therefore lower statistics and higher noise) at which is scanned, the reconstruction quality is reduced. One method to improve reconstruction quality is using a priori knowledge. Of the two most used reconstruction algorithms, the iterative reconstruction scheme is best suited for this. The simultaneous algebraic reconstruction technique or SART starts from a (typically empty) volume and improves this gradually by back projecting the difference between a simulated projection from this volume and the measured projection. The resulting volume is used for the next iteration step. After a number of iterations, the solution converges to the final volume which represents the sample. In this research, this algorithm is used and adapted to take prior knowledge into account. Prior knowledge can take various forms. Using an initial volume (to start the reconstruction algorithm with) that resembles the sample is the most well-known and already presents a great improvement. This can be a volume that is reconstructed from a previous scan of the same sample, before the dynamic process is initiated, or one from after the process has finished. It is also possible to incorporate information in the algorithm about the regions in the volume where the changes are most likely to occur. The voxels in these regions are assigned a higher contribution from the back projection in comparison with their 'static' neighboring voxels which are assumed to be valid in the initial volume. This reduces the number of projections needed significantly. These forms of prior knowledge already pose a great improvement to the reconstruction quality, as is shown by the preliminary results. There are however numerous other possibilities to improve the reconstruction of dynamic processes. Other forms of prior knowledge, e.g. the continuity of changes or external measurements, can be included. Spatio-temporal correlations present another way to improve 4D-reconstruction. The projections will no longer be divided into completely separate subsets. Instead, the correlations between different projections will be used. This means that projections 'far' away from the time point that is being reconstructed will also (partially) be included. In this way the limitation of a small subset is (partially) removed, since much larger sets of projections are considered. The reconstructions that lie some time away from the reconstruction point cannot be straightforwardly included, since this would include exactly the artefacts that made the scanning of dynamic processes hard in the first place. This is a subject of further and current research. REFERENCES [1]\0009M. Beister, D. Kolditz, W. A. Kalender, textquotedblleftIterative reconstruction methods in X-ray CT,textquotedblright Physica Medica, vol. 28, no. 2, pp. 94-108, Apr. 2012. [2]\0009S. Berg, H. Ott, S. A. Klapp, A. Schwing, R. Neiteler, N. Brussee, A. Makurat, L. Leu, F. Enzmann, J.-O. Schwarz, textquotedblleftReal-time 3D imaging of Haines jumps in porous media flow,textquotedblright Proc Natl Acad Sci U S A, vol. 110(10), pp. 3755--3759, Mar. 2013. [3]\0009T. Bultreys, M. A. Boone, M. N. Boone, T. De Schryver, B. Masschaele, L. Van Hoorebeke, V. Cnudde, textquotedblleftFast laboratory-based micro-computed tomography for pore-scale research: illustrative experiments and perspectives on the future,textquotedblright Adv. Wat. Res., In Press. Available online May 2015. [4]\0009V. Cnudde, M. N. Boone, textquotedblleftHigh-resolution X-ray computed tomography in geosciences: A review of the current technology and applications,textquotedblright Earth-Science Reviews, vol. 123, pp. 1-17, Aug. 2013. [5]\0009G. Van Eyndhoven, K. J. Batenburg, J. Sijbers, textquotedblleftRegion-based iterative reconstruction of structurally changing objects in CTtextquotedblright, IEEE Trans. Image Processing, vol. 23, no. 2, pp. 909-919, Feb. 2014. [6]\0009L. Brabant, textquotedblleftLatest developments in the improvement and quantification of high resolution X-ray tomography data,textquotedblright Ph.D. dissertation, Dep. Phys. and Astr., Fac. Sciences, Ghent Univ., Ghent, Belgium, 2013.