Date of Award


Degree Name

Doctor of Philosophy



First Advisor

Dr. Rajib Paul

Second Advisor

Dr. Magdalena Niewiadomska-Bugaj

Third Advisor

Dr. Joseph McKean

Fourth Advisor

Dr. Kathleen Baker


Brain image, image smoothing, spatial models, MRI denoising, random effect model, spatial smoothing


Spatial smoothing in Magnetic Resonance image (MRI) involves applying a filter to remove high frequency information and consequently improves signal-to-noise ratio that can greatly aid neurosurgeons in pre-surgical planning stages of tumor resection. This immensely reduces the time spent on Electrical stimulation mapping (ESM) prior to surgery. MRI's three-dimensional data provides voxel intensities with complex spatial relationship. The standard de facto spatial smoothing method, Gaussian Kernel smoothing, is satisfactory since a uniform smoothing is done for the whole brain. Secondly, the kernel smoothing technique assumes normality for the voxel intensity, but there is ample evidence in current research that indicates that voxel intensities for MRI data approximately follow a Racian Distribution. This leads to a blurring effect when the kernel smoother is applied to MRI data at various bandwidths. Due to the nature of the brain, we must consider the various tissue types and regions in any smoothing algorithm and hereby avoid blurring region borders. This study developed a flexible reduced rank spatial smoothing technique that achieves data reduction and sensible spatial smoothing at the same time. To achieve this, a reduced rank spatial model in the Bayesian framework with spherical basis function at specified knot locations with different spatial resolutions is developed. Knot locations are equidistant but with careful consideration of the anatomical structure of the brain which mimics a half sphere. The data used is a public sourced MRI data of an adult male with brain tumors or lesions to the left region of his brain. Twenty-two slices of 512 by 512 voxel images were acquired totaling close to 6 million data points. This model structure aids in attaining a relatively manageable covariance structure in a computational sense. This study set out to achieve smoothing MRI for the entire brain and in the process of doing so, to achieve data reduction. For preliminary analysis, we consider a single slice of brain image (T-1 weighted). This forms a 2D image. In this case, we use a modified bisquare basis function to explain the small scale variability in our model. This model realized a Signal-to-noise ratio (SNR) improvement of about 22.5% over the current pre-processed data set. In the second half of our model, we demonstrate the flexible nature of our spatial model in smoothing the region where possible tumor or lesion spots can be observed from the image. Adjacent slices are treated as layers of time series and a first order structure is used to determine association between slices. We use marginally non-informative prior for the covariance matrix of the reduced dimension latent process in our model. As opposed to the kernel smoothing method, a normal distribution was not imposed on the latent process. Instead we use a Gaussian mixture that can take care of the heavy tailed behaviors as demonstrated in MRI data sets. The proposed method demonstrates an improvement in the automated spatial smoothing process for the Brainix MRI data. This method can be beneficial to the brain surgeon in that it significantly reduces the time spent probing via ESM as region boundary blurring is avoided.

Access Setting

Dissertation-Open Access