Regularized iterative reconstruction in tensor tomography using gradient constraints

This paper investigates the iterative reconstruction of tensor fields in diffusion tensor magnetic resonance imaging (MRI). The gradient constraints on eigenvalue and tensor component images of the diffusion tensor were exploited. A computer-generated phantom was used in order to simulate the diffusion tensor in a cardiac MRI study with a diffusion model that depends on the fiber structure of the myocardium. Computer simulations verify that the regularized methods provide an improved reconstruction of the tensor principal directions. The reconstruction from experimentally acquired data is also presented.