Gaussian Process models for respiratory motion compensation

In robotic radiotherapy, the precise irradiation of moving tumours is possible with technicalsystems like Vero or CyberKnife ® Synchrony. Time latencies have to be considered to performreal-time treatments, which can be compensated by time series prediction of optical markers.Recently, relevance vector machines (RVM) have been investigated for this problem [1]. Theprediction accuracy of this probabilistic method was superior compared to several non-probabilistic methods like Support Vector regression (SVR) and wavelet based least meansquare (wLMS). As each predicted point of RVM is the mean of a normal distribution, thepredicted variance can be used as additional safety feature indicating the “certainty” of thealgorithm. Here, we want to investigate Gaussian Process (GP) models, which are ageneralization of RVM with distinct advantages. First, an arbitrary prediction horizon can beselected. Second, prior knowledge of the function behaviour can be easily included. Third, GPscan be easily extended to multi-dimensional and multitask models. We focus on the selectionof the optimal covariance function.