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This paper presents novel single and multi-shell sampling schemes fordiffusion MRI. In diffusion MRI, it is paramount that the number of samples isas small as possible in order that scan times are practical in a clinicalsetting. The proposed schemes use an efficient number of measurements in thatthe number of samples is equal to the degrees of freedom in the orthonormalbases used for reconstruction. Novel reconstruction algorithms based on smallersubsystems of linear equations, as compared to the standard regularizedleast-squares method, are developed for both single and multi-shells samplingschemes. The smaller matrices used in these novel reconstruction algorithms aredesigned to be well-conditioned, leading to improved reconstruction accuracy.Accurate and robust reconstruction is also achieved through incorporation ofregularization into the novel reconstruction algorithms and using a Rician ornon-central Chi noise model. We quantitatively validate our single andmulti-shell schemes against standard least-squares reconstruction methods toshow that they enable more accurate reconstruction when the number of samplesis equal to the degrees of freedom in the basis. Human brain data is also usedto qualitatively evaluate reconstruction

Efficient sampling and robust 3D diffusion magnetic resonance imaging signal reconstruction