The Power Analysis of Sparse Representation based on Laplace-Beltrami eigenfunctions

In localizing a group difference or a covariate of a factor of interest on structure model in invivo human brains using magnetic resonance imaging (MRI), various approaches have been used. For approaches that analyze the local differences voxel-wisely, voxel-based morphometry (VBM), deformation-based morphometry (DBM) and tensor-based morphometry (TBM) have been proposed [1, 7, 2]. In these methods, the local measure of brain tissue for a voxel is quantified. In VMB, the probability of certain tissue such as gray matter is used as a gray matter density that quantifies local integrity of gray matter of a corresponding voxel. In TBM, the local volume is quantified as Jacobian determinant of deformation vector field that deforms the template volume to an individual volume. Then the difference of local measures at each voxel usually is tested by a general linear model (GLM) while the family-wise error rate is controlled by statistical techniques such as false discovery rate (FDR) or random field theory (RFT).