Magnetic Resonance Imaging (MRI), along with its extension, Diffusion-Weighted MRI, is a noninvasive imaging modality which has become popular for clinical and research purposes. The raw data obtained from the MRI scanner may not be immediately usable by the health professional, thereby creating the need for additional methods to make more sensible representations of the data and extract the desired information from them. This thesis introduces a few new reconstruction, post-processing, and analysis techniques in diffusion and anatomical MRI, as described next.

Hardware, timing, and SNR considerations restrict the slice-selection and the in-plane resolutions of MRI differently, generally resulting in anisotropic voxels. This non-uniform sampling can be problematic, especially in image segmentation and clinical examination. To alleviate this, the acquisition is divided into (two or) three separate scans, with thick slices yet orthogonal slice-selection directions. In the first part of the thesis, a non-iterative wavelet-based approach to combining the three orthogonal scans is adopted, and its advantages compared to other existing methods, such as Fourier techniques, are mentioned, including the consideration of the actual pulse response of the MRI scanner and lower computational complexity.

Estimating the thickness of the cerebral cortex is a key step in many brain imaging studies, revealing valuable information on development or disease progression. In the second part, a framework for measuring the cortical thickness, based on minimizing line integrals over the probability map of the gray matter in the MRI volume is presented. In contrast to the proposed approach, previous methods often perform a binary-valued hard segmentation of the gray matter before measuring the cortical thickness. Due to image noise and partial volume effects, such a hard classification ignores the underlying tissue class probabilities assigned to each voxel, discarding potentially useful information. The performance of the method is demonstrated on both artificial volumes and real 3D brain MRI data from subjects with Alzheimer's disease and healthy individuals.

Q-ball imaging (QBI) is a Diffusion MRI reconstruction technique which has been proven very successful in resolving multiple intravoxel fiber orientations in MR images. The standard computation of the orientation distribution function (ODF, the probability of diffusion in a given direction) from q-ball data uses linear radial projection, neglecting the change in the volume element along each direction, resulting in artificial blurring of the ODFs. In the third part of this dissertation, a new technique is proposed that, by considering the solid angle factor, uses the mathematically correct definition of the ODF and results in a dimensionless and normalized ODF expression. In addition, a semi-analytic ODF maxima extraction algorithm is provided, and a measure for fiber crossing is also introduced which is shown to be related to the intelligence quotient. The performances of the proposed techniques are demonstrated on artificial examples and high-resolution real data acquired at 7 Tesla.

In the fourth part, a global probabilistic fiber tracking approach based on the voting process provided by the Hough transform is introduced. The proposed framework tests candidate 3D curves in the volume, assigning to each one a score computed from the diffusion images, and then selects the curves with the highest scores as the potential anatomical connections. The algorithm avoids local minima by performing an exhaustive search at the desired resolution, and is easily extended to multiple subjects. Experimental results are presented on HARDI volumes, ranging from simulated and 1.5T physical phantoms to 7T and 4T human brain and 7T monkey brain datasets.