Decoupling of imaging and diffusion gradients in DTI

The linear algebra framework for MR-DTI introduced in the companion manuscript is expanded to a normed space structure. The issues originating from the inclusion of imaging gradients into the MR-DTI model to obtain a fuller description are tackled by the optimization theory. A sample independent, geometric objective function based on matrix norms is defined. A parametrization of feasible diffusion gradient sets is presented so that the optimization can be carried out by making sure that the coefficient matrix for the estimation equations has full rank. The experiments are carried with the optimal gradient schemes. There are significant improvements in terms of model matching error and the lowering of the difference between eigenvalues calculated with or without the imaging gradients.