Scientific visualization of tensor fields is challenging due to the complex and multivariate nature of tensor data. The visualization of multiple tensor fields becomes even more difficult, and still in its infancy. This thesis aims at contributing visual analysis techniques for multiple 3D tensor fields. We focus specifically on the visual analysis of Diffusion Tensor Imaging (DTI) datasets. DTI is a magnetic resonance imaging (MRI) based modality, which is commonly used in neuroscience to investigate brain white matter in vivo. It requires a long scanning time compared to other imaging modalities. Acceleration of MRI acquisitions has the potential to improve the applicability of DTI. Compressed sensing (CS) is a signal reconstruction technique that is used to accelerate MRI acquisitions. The traditional CS method aims at optimizing the global quality of the reconstructed image. However, in practice, the quality of local structures is often of more interest. Therefore, we investigate CS for this purpose and contribute in this direction by adapting the traditional CS reconstruction method to focus on the quality of local structures.

Diffusion Tensor Imaging (DTI) group studies often require the comparison of two groups of 3D diffusion tensor fields. The total number of datasets involved in the study and the multivariate nature of diffusion tensors together make this a challenging process. The traditional approach is to reduce the six-dimensional diffusion tensor to some scalar quantities, which can be analyzed with univariate statistical methods, and visualized with standard techniques such as slice views. However, this provides merely part of the whole story due to information reduction. If to take the full tensor information into account, only few methods are available, and they focus on the analysis of a single group, rather than the comparison of two groups. Simultaneously comparing two groups of diffusion tensor fields by simple juxtaposition or superposition is rather impractical. In this work, we extend previous work by Zhang et al. [ZCH17] to visually compare two groups of diffusion tensor fields. To deal with the wealth of information, the comparison is carried out at multiple levels of detail. In the 3D spatial domain, we propose a details-on-demand glyph representation to support the visual comparison of the tensor ensemble summary information in a progressive manner. The spatial view guides analysts to select voxels of interest. Then at the detail level, the respective original tensor ensembles are compared in terms of tensor intrinsic properties, with special care taken to reduce visual clutter. We demonstrate the usefulness of our visual analysis system by comparing a control group and an HIV positive patient group.