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Brain imaging has the potential to advance our understanding of human health and to improve diagnosis and treatment of neurological diseases. Inspired by key questions in neuroscience and medicine, it becomes extremely important to develop statistical methods that can accurately and efficiently recover useful quantitative information from large amounts of brain images. The underlying computational issues are challenging and often hampered by uncertainties in imaging acquisition parameters, the variability of human anatomy and physiology, as well as the nature of the imaging data to be handled such as the presence of noise and correlation, and the sample and data sizes, and so on. Structural and Functional MRI (sMRI and fMRI) Among the varieties of brain imaging modalities, magnetic resonance imaging (MRI) is primarily a noninvasive imaging technique used in radiology to visualize the brain’s structure and function. Two main forms of MRI include: Structural MRI (sMRI) images the anatomy and strucure of the brain (Symms et al., 2004) and provides detailed pictures of the brain’s size and shape; functional MRI (fMRI) identifies active regions, patterns of functional connectivities during either tasks specifically designed to study various aspects of brain fundtion or during the resting state (Martijn et al., 2010). The MRI machine is, in essence, a big magnet. As the subject lies in its magnetic field, invisible radio waves are released around the subject. This will result in harmless radio waves bouncing off the different substances that make up the brain. The radio waves are then detected by a computer, which transforms the data into images of the brain’s structure and activity. In fMRI, as the subject lies in the MRI machine, simple tasks are given; the MRI then maps what parts of the brain are most active during those tasks compared with activity while the brain is at rest. This allows researchers to understand how the brain functions. This information is used together with the data from the sMRI data to reveal a comprehensive picture of brain structure and function that fit in the overall studies or to allow us to understand how the healthy brain works. The informaiton and fusion of structural and functional MRI can also improve our understanding and the treatment of neurodegenerative diseases and mental disorders such as Alzheimer’s disease and schizophrenia. Brain Morphometry Analysis with Hypothesis Testing from Structural MRI Structural MRI (sMRI), or simply called MRI, scans are usually stored in the format of threedimensional (3D) voxels. There are several procedures for MRI post-processing, and the two

Statistical Analysis for Recovery of Structure and Function from Brain Images