Smoothing in Magnetic Resonance Image Analysis and a Hybrid Loss for Support Vector Machine

This thesis will focus on applying smoothing splines to magnetic resonance image (MRI) analysis. Some additional work on support vector machine with a hybrid loss function will be discussed. We apply smoothing splines to both the structural MRI and functional MRI. For the structural MRI, we fit thin plate splines to overlapping blocks of the image with different configurations of knots. The optimal configurations are found by the generalized cross validation with a constant factor (Luo and Wahba, 1997). The fitted splines with the optimal configurations are then blended to get a smoothed image of the brain. Thresholds are found along the way with k-means algorithm and are blended as well. By thresholding the blended image we obtained, we get the boundaries between gray matter, white matter, cerebrospinal fluid, and others. The combination of smoothing and thresholding gives us very good results in terms of segmentation. For the functional magnetic resonance image analysis, we propose a partial spline model for the model fitting and hypothesis testing. Simulation are done to test the theoretical properties of the model. It appears that the partial spline model can compete with the commonly used smoothing+GLM paradigm. A support vector machine with a new hybrid loss is studied in the thesis. We propose a loss function that is a hybrid of the hinge loss and the logistic