Image reconstruction using shift-variant resampling kernel for magnetic resonance imaging

Nonrectilinear k-space trajectories are often used in MRI applications due to their inherent fast acquisition and immunity to motion and flow artifacts. In this work, we develop a more general formulation for the problem of resampling under the same assumptions as previous techniques. The new formulation allows the new technique to overcome the present problems with these techniques while maintaining a reasonable computational complexity. The image space is decomposed into a complete set of orthogonal basis functions. Each function is sampled twice, once with a rectilinear trajectory and the other with a nonrectilinear trajectory resulting in two vectors of samples. The mapping matrix that relates the two sets of vectors is obtained by solving the set of linear equations obtained using the training basis set. In order to reduce the computational burden at the reconstruction time, only a few nonrectilinear samples in the neighborhood of the point of interest are used. The proposed technique is applied to simulated data and the results show a superior performance of the proposed technique in both accuracy and noise resistance and demonstrate the usefulness of the new technique in the clinical practice.