Diffusion tensor MR image restoration

Diffusion tensor magnetic resonance imaging (DT-MRI) can provide the fundamental information required to visualize structural connectivity. However, this high-dimensional data can be rather noisy and requires restoration. In this paper, we present a novel unified formulation involving a variational principle for simultaneous smoothing and estimation of the diffusion tensor field from DT-MRI. This tensor field is estimated directly from the measurements using a combination of L-P smoothness and positive definiteness constraints respectively. The data term we employ is the Stejskal-Tanner equation instead of its linearized version as usually employed in the published literature. In addition, we impose the positive definite constraint via the Cholesky decomposition of the tensors in the field. Our unified variational principle is discretized and solved numerically using the limited memory quasi-Newton method. Algorithm performance is depicted via both synthetic and real data experiments.