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.