Carl-Fredrik Westin1, Ofer Pasternak2, Hans Knutsson3
1Department of Radiology , BWH, Harvard Medical School, Boston, MA, United States; 2Department of Radiology, BWH, Harvard Medical School, Boston, MA, United States; 3Department of Biomedical Engineering, Medical Informatics, Linkping University, Linkping, Sweden
Minimizing the error propagation that a diffusion MRI gradient scheme introduces is an important task in the design of robust and un-biased experiments. We propose two schemes for the construction of rotationally invariant multiple-shells. The first is a dual frame method that optimizes the rotation invariance of any set of samples. The second uses a subset of the icosahedral set that can intuitively be used for nested rotationally invariant schemes with pre-defined number of samples. Rotationally invariance produces orientationally unbiased estimates and reduces the correlation of the samples, which is an important feature for reconstruction methods such as multiple shells and compressed sensing.