Determinant of the information matrix: A new rotation invariant optimality metric to design gradient encoding schemes

Minimum condition number (CN) gradient encoding scheme was introduced to diffusion MRI community more than a decade ago. It's computation requires tedious numerical optimization which usually leads to sub-optimal solutions. The CN does not reflect any benefits in acquiring more measurements, i.e. it's optimal value is constant for any number of measurements. Further, it is variable under rotation. In this paper we (i) propose an accurate method to compute minimum condition number scheme; and (ii) introduce determinant of the information matrix (DIM) as a new opti-mality metric that scales with number of measurements and does reflect what one would gain from acquiring more measurements. Theoretical analysis shows that DIM is rotation invariant. Evaluations on state-of-the-art encoding schemes proves the relevance and superiority of the proposed metric compared to condition number.