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Table of contents
1 Introduction
1.1 Leksell Gamma Knife
1.2 Cone Beam Computed Tomography
1.2.1 Scatter Artefacts in CBCT Images
1.3 Scientific Computation on GPUs
1.4 Layout of thesis
2 Background
2.1 CUDA
2.2 Monte Carlo Method
2.3 Photon Transport in Matter
2.4 The Monte Carlo Method for Photon Transport
2.4.1 Related Work
2.4.2 Variance Reduction Techniques
2.4.3 Pre- and Post-Processsing
2.4.4 Random Number Generation
3 Method
3.1 CBCT Volume Reconstruction with Scatter Reduction
3.2 Geometry
3.2.1 Material Model
3.3 Simulating Photons
3.3.1 Generating Photons
3.3.2 Advance Photon
3.3.3 Score Photon
3.3.4 Simulating Interactions
3.3.5 Energy Cut-off
3.4 Variance Reduction
3.4.1 Splitting
3.4.2 Russian Roulette
3.4.3 Forced Detection
3.5 Filtering Methods
3.6 Scatter Removal
3.7 Code Optimizations and Details
3.7.1 Random Number Generation
3.7.2 Memory Use and Accesses
3.7.3 Built-in Function Calls
3.7.4 Thread Coherence
3.7.5 Numerical Precision
4 Results
4.1 Performance
4.1.1 Variance Reduction Methods
4.2 Physical Accuracy
4.2.1 PENELOPE comparison
4.2.2 Head phantom
4.3 Effect on reconstruction
5 Discussion
5.1 Performance
5.1.1 Variance Reduction
5.2 Accuracy
5.3 Reconstruction
6 Conclusions
6.1 Further work
6.1.1 Sources of error
6.1.2 Possible Speed-ups
Bibliography
A Rejection Sampling
B Estimation of Memory Limitations
