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Icosahedral gradient encoding scheme for an arbitrary number of measurements

The icosahedral gradient encoding scheme (GES) is widely used in diffusion MRI community due to its uniformly distributed orientations and rotationally invariant condition number. The major drawback with this scheme is that it is not available for arbitrary number of measurements. In this paper (i) we propose an algorithm to find the icosahedral scheme for any number of measurements. Performance of the obtained GES is evaluated and compared with that of Jones and traditional icosahedral schemes in terms of condition number, standard deviation of the estimated fractional anisotropy and distribution of diffusion sensitizing directions; and (ii) we introduce minimum eigenvalue of the information matrix as a new optimality metric to replace condition number. Unlike condition number, it is proportional to the number of measurements and thus in agreement with the intuition that more measurements leads to more robust tensor estimation. Furthermore, it may independently be maximized to design GESs for different diffusion imaging techniques.