Patent ID: 7821262

Claim:
A magnetic resonance tomography apparatus comprising: a magnetic resonance data acquisition system configured to interact with a subject to acquire measured, raw magnetic resonance data from the subject; a computer that enters said measured, raw magnetic resonance data into k-space by multi-dimensionally undersampling k-space along a plurality N of basic partial trajectories τ o in k-space, said N basic partial trajectories τ o , in combination, forming a geometric arrangement of source points, and that determines a plurality M of different operators C m (Δ k m ), with each operator representing an algebraic transformation through which unmeasured target points at an interval Δ k n from one of said source points are synthesized from a plurality of said source points, and that applies said operators C m (Δ k m ) to at least one subset of said source points for at least partial completion of a magnetic resonance data set; and an image reconstruction computer that reconstructs substantially artifact-free image in three-dimensional space from said source points and said synthesized target points in said magnetic resonance data set.