Reconstructing MR Images from Under-or Unevenly-Sampled k-Space

In MRI, non-rectilinear sampling trajectories are applied in k-space to enable faster imaging. Traditional image reconstruction methods such as a fast Fourier transform (FFT) can not process datasets sampled in non-rectilinear forms (e.g., radial, spiral, random, etc.) and more advanced algorithms are required. The Fourier reduction of optical interferometer data (FROID) algorithm is a novel image reconstruction method 1-3 proven to be successful in reconstructing spectra from sparsely and unevenly sampled astronomical interferometer data. The framework presented allows a priori information, such as the locations of the sampled points, to be incorporated into the reconstruction of images. In this paper, the FROID algorithm has been adapted and implemented to reconstruct magnetic resonance (MR) images from data acquired in k-space where the sampling positions are known. Also, simulated data, including randomly sampled data, are tested and analyzed.