  Purpose: To enable rigid-body motion tolerant parallel volumetric magnetic
resonance imaging by retrospective head motion correction on a variety of
spatio-temporal scales and imaging sequences. Theory and methods: Tolerance
against rigid-body motion is based on distributed and incoherent sampling
orders for boosting a joint retrospective motion estimation and reconstruction
framework. Motion resilience stems from the encoding redundancy in the data, as
generally provided by the coil array. Hence, it does not require external
sensors, navigators or training data, so the methodology is readily applicable
to sequences using 3D encodings. Results: Simulations are performed showing
full inter-shot corrections for usual levels of in-vivo motion, large number of
shots, standard levels of noise and moderate acceleration factors. Feasibility
of inter- and intra-shot corrections is shown under controlled motion in-vivo.
Practical efficacy is illustrated by high quality results in most corrupted of
208 volumes from a series of 26 clinical pediatric examinations collected using
standard protocols. Conclusion: The proposed framework addresses the rigid
motion problem in volumetric anatomical brain scans with sufficient encoding
redundancy which has enabled reliable pediatric examinations without sedation.
