MR Image Reconstruction from Pseudo-Hex Lattice Sampling Patterns Using Separable FFT

— Common MRI sampling patterns in kspace, such as spiral trajectories, have nonuniform density and do not lie on a rectangular grid. We propose mapping the sampled data to a pseudo-hex lattice, taking advantage of its approximate isotropic nature in k-space and square nature in the reconstructed image space. The group structure of the lattice is exploited to implement the Fourier transform computations on the data using a separable FFT algorithm, which provides signi…cant computational ef…ciency. We suggest this method can be generalized to multiresolution lattices, in which the signal is represented in di¤erent regions in k-space with varying sampling densities. The operations on index sets and mapping to separable FFT can be implemented e¢ ciently in software or custom hardware (e.g., FPGA).