MS-FRACT: Optimized linear transform methods for ODF estimation in multi-shell diffusion MRI

This paper proposes a new linear transform approach for multi-shell ODF estimation that has been theoretically characterized and does not require modeling assumptions. The proposed approach, called MS-FRACT, is optimized over the class of all rotationally-invariant linear transforms to yield accurate ODFs. Due to linearity, MS-FRACT yields stable and predictable results, and can be directly interpreted with respect to the true diffusion propagator. The performance of MS-FRACT is illustrated using simulated and real data. In addition to proposing MS-FRACT, a new theoretical framework is also described that can be applied to arbitrary multi-shell linear ODF estimation methods.