Intensity modulated proton therapy is an advanced radiotherapy technique that is used to treat cancer patients. In order to successfully treat a patient, sufficient dose to the tumor is required. However, during the fractionated treatment, multiple errors can cause a difference between the planned and actual dose delivery. To ensure adequate dose delivery in potential error scenarios, robust treatment plans are acquired as these are less sensitive to uncertainties inherent to proton therapy. However, robust optimization is challenging.

First, as robust optimization accounts for multiple error scenarios, the time needed to generate optimal treatment plans increases significantly. Therefore, it is investigated in this thesis if the optimization time can be reduced while preserving treatment plan quality. This is investigated through two different methods. In the first method, the number of error scenarios accounted for during optimization is reduced. We found that this can significantly reduce optimization time, while improved target coverage and lower risk on side effects are obtained. However, the near-maximum dose to the tumor was found to be less favourable. The second method investigated is variance optimization. This method significantly reduces optimization time. However, for similar target coverage, the risk of side effects increases.

Another challenge related to robust optimization is the increase in delivered dose to healthy tissues surrounding the tumor, which increases the risk of side effects. Therefore, it is investigated in this thesis if the risk of side effects can be lowered by allowing higher maximum dose to the tumor. It is found that this method indeed reduces the risk of side effects. However, the increased maximum dose to the tumor may not be clinically desired as the increase may lead to higher risks of other side effects: edema and fibrosis. The clinically desired trade-off between near-maximum dose and normal tissue sparing should be established.

MRI images are very useful for detecting diseases, as well as for the treatment of diseases. However, MRI scanners are usually too expensive for developing countries to purchase and maintain. Therefore, a less expensive scanner is being developed at Delft University of Technology and Leiden University Medical Center. Unfortunately, the images which are generated by this low-cost MRI scanner are contaminated by noise. The MRI images are determined by solving a system of equations of the form Ax= y, where x is the unknown image. As this system is perturbed, regression methods can be applied in order to find the best approximate value of x. The ordinary least squares method solves this system for perturbations in y. Whereas in the MRI case, it appears that both A and y are perturbed. The total least squares method is often used in order to solve these kind of perturbed systems of equations. The aim of this thesis is to investigate the abilities of this method for the purpose of noise reduction in MRI images. It appears that the total least squares method in combination with regularization operators is able to cancel out a certain amount of noise from the images. However, no significant advantages compared to the ordinary least squares method are found.