Simultaneous Smoothing and Estimation of the Tensor Field from Diffusion Tens or MRI

Diffusion tensor magnetic resonance imaging (DT-MRI) is a relatively new imaging modality in the field of medical imaging. This modality of imaging allows one to capture the structural connectivity if any between functionally meaningful regions for example, in the brain. The data however can be noisy and requires restoration. In this paper, we present a novel unified model for simultaneous smoothing and estimation of diffusion tensor field from DT-MRI. The diffusion tensor field is estimated directly from the raw data with smoothness and positive definiteness constraints. The data term we employ is from the original StejskalTanner equation instead of the linearized version as usually done in literature. In addition, we use Cholesky decomposition to ensure positive definiteness of the diffusion tensor. The unified model is discretized and solved numerically using limited memory Quasi-Newton method. Both synthetic and real data experiments are shown to depict the algorithm performance.