Tensor MRI Regularization via Graph Diffusion

A new method for diffusion tensor (DT) image regularization is presented that relies on heat diffusion on discrete structures. We represent a DT image using a weighted undirected graph, where the weights of the edges are determined from the geometry of the white matter ber pathways. Diffusion across this weighted graph is captured by the heat equation, and the solution, i.e. the heat kernel, is found by exponentiating the Laplacian eigen-system with time. DT image regularization is accomplished by convolving the heat kernel with each component of the diffusion tensors, and its numerical implementation is realized by using the Krylov subspace technique. The algorithm is tested and analyzed both on synthetic and real DT images.