Regularization For MR Diffusion Inverse Problems

In this presentation, we introduce a novel method of regularizing the reconstruction of fiber directions from diffusion images. Diffusion Tensor Imaging (DTI) is a technique which extracts information from multiple Magnetic Resonance Images about the amount and orientation of diffusion within the body. It is used for brain connectivity studies, providing fundamental information about the white matter structure, and indirectly about function. Many methods have been represented in the literature for estimating diffusion tensors with and without regularization. The previous methods of regularization are subject to problems such as information loss and lack of coherency in the measured results. The method we introduce in this presentation aims to improve the quality of reconstructed fiber directions by (1) using a new model for diffusion, which can be interpreted as a restriction of the diffusion tensor model, but in which the principal eigenvalue of the diffusion tensor is a model variable and not a derived quantity; and (2) using regularizing terms which penalize non-smoothness in the principal diffusion direction directly. This method is the first one to combine a modern regularization technique with a single-fiber reconstruction. It could be used directly for bulk coherent fiber (e.g. muscle) visualization, or form the basis of new tracking algorithms.