title: Reconstruction of MR images from data acquired on a general nonregular grid by pseudoinverse calculation.
abstract: A minimum-norm least-squares image-reconstruction method for the reconstruction of magnetic resonance images from non-Cartesian sampled data is proposed. The method is based on a general formalism for continuous-to-discrete mapping and pseudoinverse calculation. It does not involve any regridding or interpolation of the data and therefore the methodology differs fundamentally from existing regridding-based methods. Moreover, the method uses a continuous representation of objects in the image domain instead of a discretized representation. Simulations and experiments show the possibilities of the method in both radial and spiral imaging. Simulations revealed that minimum-norm least-squares image reconstruction can result in a drastic decrease of artifacts compared with regridding-based reconstruction. Besides, both in vivo and phantom experiments showed that minimum-norm least-squares image reconstruction leads to contrast improvement and increased signal-to-noise ratio compared with image reconstruction based on regridding. As an appendix, an analytical calculation of the raw data corresponding to the well-known Shepp and Logan software head phantom is presented.
authors.affiliation: Department of Electronics and Information Systems, Ghent University, Belgium. rik.vandewalle@rug.ac.be
authors.forename: R
authors.initials: R
authors.lastname: Van de Walle
authors.forename: H H
authors.initials: HH
authors.lastname: Barrett
authors.forename: K J
authors.initials: KJ
authors.lastname: Myers
authors.forename: M I
authors.initials: MI
authors.lastname: Altbach
authors.forename: B
authors.initials: B
authors.lastname: Desplanques
authors.forename: A F
authors.initials: AF
authors.lastname: Gmitro
authors.forename: J
authors.initials: J
authors.lastname: Cornelis
authors.forename: I
authors.initials: I
authors.lastname: Lemahieu
mesh_terms: D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging